sunyiyou/math_combinatory_probability_no_specific_letter_fixed_level_1

messages listlengths 1 1	ground_truth stringclasses 2 values	dataset stringclasses 1 value
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {k: 2, e: 1, i: 1}, shuffle the letters in the word, what is the probability of no letter 'k' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {g: 1, m: 2, v: 1}, shuffle the letters in the word, what is the probability of no letter 'm' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {w: 2, k: 1, u: 1}, shuffle the letters in the word, what is the probability of no letter 'k' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {f: 1, q: 1, n: 2}, shuffle the letters in the word, what is the probability of no letter 'q' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {n: 2, s: 1, e: 1}, shuffle the letters in the word, what is the probability of no letter 's' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {m: 2, c: 1, x: 1}, shuffle the letters in the word, what is the probability of no letter 'x' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {d: 2, i: 1, k: 1}, shuffle the letters in the word, what is the probability of no letter 'k' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {u: 1, r: 1, d: 2}, shuffle the letters in the word, what is the probability of no letter 'd' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {h: 2, l: 1, w: 1}, shuffle the letters in the word, what is the probability of no letter 'l' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {w: 1, i: 2, u: 1}, shuffle the letters in the word, what is the probability of no letter 'u' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {p: 2, z: 1, h: 1}, shuffle the letters in the word, what is the probability of no letter 'p' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {f: 1, k: 1, s: 2}, shuffle the letters in the word, what is the probability of no letter 'f' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {m: 2, o: 1, l: 1}, shuffle the letters in the word, what is the probability of no letter 'o' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {k: 1, o: 2, g: 1}, shuffle the letters in the word, what is the probability of no letter 'k' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {f: 1, h: 2, b: 1}, shuffle the letters in the word, what is the probability of no letter 'h' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {m: 2, c: 1, w: 1}, shuffle the letters in the word, what is the probability of no letter 'm' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {z: 1, l: 1, a: 2}, shuffle the letters in the word, what is the probability of no letter 'l' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {d: 1, z: 2, x: 1}, shuffle the letters in the word, what is the probability of no letter 'z' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {n: 1, r: 1, h: 2}, shuffle the letters in the word, what is the probability of no letter 'h' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {a: 2, s: 1, d: 1}, shuffle the letters in the word, what is the probability of no letter 's' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {s: 2, o: 1, z: 1}, shuffle the letters in the word, what is the probability of no letter 'o' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {j: 1, l: 1, o: 2}, shuffle the letters in the word, what is the probability of no letter 'j' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {m: 1, d: 2, w: 1}, shuffle the letters in the word, what is the probability of no letter 'w' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {i: 1, r: 2, k: 1}, shuffle the letters in the word, what is the probability of no letter 'i' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {g: 1, z: 2, s: 1}, shuffle the letters in the word, what is the probability of no letter 'g' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {b: 1, r: 2, y: 1}, shuffle the letters in the word, what is the probability of no letter 'y' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {g: 2, l: 1, j: 1}, shuffle the letters in the word, what is the probability of no letter 'g' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {k: 2, z: 1, g: 1}, shuffle the letters in the word, what is the probability of no letter 'g' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {s: 2, y: 1, x: 1}, shuffle the letters in the word, what is the probability of no letter 'y' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {u: 2, l: 1, a: 1}, shuffle the letters in the word, what is the probability of no letter 'u' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {e: 1, o: 1, h: 2}, shuffle the letters in the word, what is the probability of no letter 'h' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {q: 2, j: 1, u: 1}, shuffle the letters in the word, what is the probability of no letter 'u' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {y: 1, h: 2, d: 1}, shuffle the letters in the word, what is the probability of no letter 'd' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {j: 2, g: 1, s: 1}, shuffle the letters in the word, what is the probability of no letter 's' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {a: 1, y: 1, w: 2}, shuffle the letters in the word, what is the probability of no letter 'w' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {t: 1, m: 2, b: 1}, shuffle the letters in the word, what is the probability of no letter 't' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {q: 1, a: 2, y: 1}, shuffle the letters in the word, what is the probability of no letter 'y' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {z: 2, y: 1, l: 1}, shuffle the letters in the word, what is the probability of no letter 'z' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {g: 1, h: 1, m: 2}, shuffle the letters in the word, what is the probability of no letter 'h' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {p: 1, s: 2, n: 1}, shuffle the letters in the word, what is the probability of no letter 'p' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {q: 1, r: 2, o: 1}, shuffle the letters in the word, what is the probability of no letter 'o' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {u: 2, i: 1, h: 1}, shuffle the letters in the word, what is the probability of no letter 'h' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {w: 1, v: 2, k: 1}, shuffle the letters in the word, what is the probability of no letter 'v' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {b: 1, v: 2, y: 1}, shuffle the letters in the word, what is the probability of no letter 'y' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {t: 1, k: 1, y: 2}, shuffle the letters in the word, what is the probability of no letter 'y' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {m: 2, a: 1, k: 1}, shuffle the letters in the word, what is the probability of no letter 'k' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {n: 1, v: 1, f: 2}, shuffle the letters in the word, what is the probability of no letter 'v' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {d: 1, w: 2, f: 1}, shuffle the letters in the word, what is the probability of no letter 'w' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {j: 1, t: 1, k: 2}, shuffle the letters in the word, what is the probability of no letter 't' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {m: 1, g: 1, r: 2}, shuffle the letters in the word, what is the probability of no letter 'r' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {q: 1, z: 1, b: 2}, shuffle the letters in the word, what is the probability of no letter 'q' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {a: 2, h: 1, t: 1}, shuffle the letters in the word, what is the probability of no letter 't' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {v: 1, o: 2, d: 1}, shuffle the letters in the word, what is the probability of no letter 'v' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {y: 1, a: 2, f: 1}, shuffle the letters in the word, what is the probability of no letter 'y' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {d: 1, p: 2, f: 1}, shuffle the letters in the word, what is the probability of no letter 'f' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {q: 1, g: 1, x: 2}, shuffle the letters in the word, what is the probability of no letter 'q' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {o: 1, a: 2, d: 1}, shuffle the letters in the word, what is the probability of no letter 'o' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {r: 1, a: 2, h: 1}, shuffle the letters in the word, what is the probability of no letter 'a' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {r: 2, h: 1, s: 1}, shuffle the letters in the word, what is the probability of no letter 's' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {o: 2, m: 1, c: 1}, shuffle the letters in the word, what is the probability of no letter 'o' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {c: 2, m: 1, z: 1}, shuffle the letters in the word, what is the probability of no letter 'z' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {f: 2, j: 1, b: 1}, shuffle the letters in the word, what is the probability of no letter 'b' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {f: 2, y: 1, n: 1}, shuffle the letters in the word, what is the probability of no letter 'n' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {d: 2, t: 1, q: 1}, shuffle the letters in the word, what is the probability of no letter 't' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {v: 1, e: 1, i: 2}, shuffle the letters in the word, what is the probability of no letter 'e' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {y: 2, c: 1, z: 1}, shuffle the letters in the word, what is the probability of no letter 'y' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {k: 2, a: 1, v: 1}, shuffle the letters in the word, what is the probability of no letter 'v' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {f: 2, z: 1, h: 1}, shuffle the letters in the word, what is the probability of no letter 'z' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {e: 2, l: 1, p: 1}, shuffle the letters in the word, what is the probability of no letter 'l' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {m: 1, v: 2, l: 1}, shuffle the letters in the word, what is the probability of no letter 'm' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {l: 2, t: 1, d: 1}, shuffle the letters in the word, what is the probability of no letter 'd' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {d: 2, w: 1, c: 1}, shuffle the letters in the word, what is the probability of no letter 'w' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {h: 1, n: 1, i: 2}, shuffle the letters in the word, what is the probability of no letter 'h' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {m: 1, q: 2, u: 1}, shuffle the letters in the word, what is the probability of no letter 'm' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {m: 2, f: 1, v: 1}, shuffle the letters in the word, what is the probability of no letter 'v' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {e: 1, u: 1, a: 2}, shuffle the letters in the word, what is the probability of no letter 'a' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {y: 2, m: 1, j: 1}, shuffle the letters in the word, what is the probability of no letter 'j' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {i: 1, u: 2, v: 1}, shuffle the letters in the word, what is the probability of no letter 'v' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {a: 2, j: 1, x: 1}, shuffle the letters in the word, what is the probability of no letter 'x' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {g: 1, e: 2, h: 1}, shuffle the letters in the word, what is the probability of no letter 'h' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {d: 1, k: 2, w: 1}, shuffle the letters in the word, what is the probability of no letter 'k' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {p: 1, q: 2, l: 1}, shuffle the letters in the word, what is the probability of no letter 'l' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {s: 1, j: 1, b: 2}, shuffle the letters in the word, what is the probability of no letter 'b' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {d: 1, n: 2, t: 1}, shuffle the letters in the word, what is the probability of no letter 't' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {q: 2, y: 1, k: 1}, shuffle the letters in the word, what is the probability of no letter 'k' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {c: 1, p: 1, e: 2}, shuffle the letters in the word, what is the probability of no letter 'e' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {c: 1, s: 2, l: 1}, shuffle the letters in the word, what is the probability of no letter 'c' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {u: 1, b: 2, q: 1}, shuffle the letters in the word, what is the probability of no letter 'q' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {l: 1, j: 2, z: 1}, shuffle the letters in the word, what is the probability of no letter 'j' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {b: 1, e: 2, c: 1}, shuffle the letters in the word, what is the probability of no letter 'c' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {o: 1, b: 2, f: 1}, shuffle the letters in the word, what is the probability of no letter 'o' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {n: 1, f: 2, r: 1}, shuffle the letters in the word, what is the probability of no letter 'r' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {h: 2, k: 1, s: 1}, shuffle the letters in the word, what is the probability of no letter 's' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {h: 1, k: 1, e: 2}, shuffle the letters in the word, what is the probability of no letter 'e' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {t: 1, x: 1, f: 2}, shuffle the letters in the word, what is the probability of no letter 'f' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	3	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {l: 1, m: 2, s: 1}, shuffle the letters in the word, what is the probability of no letter 's' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {f: 1, n: 1, c: 2}, shuffle the letters in the word, what is the probability of no letter 'n' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {o: 2, r: 1, b: 1}, shuffle the letters in the word, what is the probability of no letter 'r' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {m: 2, k: 1, z: 1}, shuffle the letters in the word, what is the probability of no letter 'z' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {d: 2, b: 1, a: 1}, shuffle the letters in the word, what is the probability of no letter 'b' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]	7	MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {k: 2, e: 1, i: 1}, shuffle the letters in the word, what is the probability of no letter 'k' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {g: 1, m: 2, v: 1}, shuffle the letters in the word, what is the probability of no letter 'm' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {w: 2, k: 1, u: 1}, shuffle the letters in the word, what is the probability of no letter 'k' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {f: 1, q: 1, n: 2}, shuffle the letters in the word, what is the probability of no letter 'q' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {n: 2, s: 1, e: 1}, shuffle the letters in the word, what is the probability of no letter 's' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {m: 2, c: 1, x: 1}, shuffle the letters in the word, what is the probability of no letter 'x' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {d: 2, i: 1, k: 1}, shuffle the letters in the word, what is the probability of no letter 'k' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {u: 1, r: 1, d: 2}, shuffle the letters in the word, what is the probability of no letter 'd' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {h: 2, l: 1, w: 1}, shuffle the letters in the word, what is the probability of no letter 'l' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {w: 1, i: 2, u: 1}, shuffle the letters in the word, what is the probability of no letter 'u' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {p: 2, z: 1, h: 1}, shuffle the letters in the word, what is the probability of no letter 'p' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {f: 1, k: 1, s: 2}, shuffle the letters in the word, what is the probability of no letter 'f' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {m: 2, o: 1, l: 1}, shuffle the letters in the word, what is the probability of no letter 'o' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {k: 1, o: 2, g: 1}, shuffle the letters in the word, what is the probability of no letter 'k' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {f: 1, h: 2, b: 1}, shuffle the letters in the word, what is the probability of no letter 'h' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {m: 2, c: 1, w: 1}, shuffle the letters in the word, what is the probability of no letter 'm' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {z: 1, l: 1, a: 2}, shuffle the letters in the word, what is the probability of no letter 'l' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {d: 1, z: 2, x: 1}, shuffle the letters in the word, what is the probability of no letter 'z' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {n: 1, r: 1, h: 2}, shuffle the letters in the word, what is the probability of no letter 'h' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {a: 2, s: 1, d: 1}, shuffle the letters in the word, what is the probability of no letter 's' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {s: 2, o: 1, z: 1}, shuffle the letters in the word, what is the probability of no letter 'o' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {j: 1, l: 1, o: 2}, shuffle the letters in the word, what is the probability of no letter 'j' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {m: 1, d: 2, w: 1}, shuffle the letters in the word, what is the probability of no letter 'w' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {i: 1, r: 2, k: 1}, shuffle the letters in the word, what is the probability of no letter 'i' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {g: 1, z: 2, s: 1}, shuffle the letters in the word, what is the probability of no letter 'g' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {b: 1, r: 2, y: 1}, shuffle the letters in the word, what is the probability of no letter 'y' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {g: 2, l: 1, j: 1}, shuffle the letters in the word, what is the probability of no letter 'g' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {k: 2, z: 1, g: 1}, shuffle the letters in the word, what is the probability of no letter 'g' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {s: 2, y: 1, x: 1}, shuffle the letters in the word, what is the probability of no letter 'y' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {u: 2, l: 1, a: 1}, shuffle the letters in the word, what is the probability of no letter 'u' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {e: 1, o: 1, h: 2}, shuffle the letters in the word, what is the probability of no letter 'h' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {q: 2, j: 1, u: 1}, shuffle the letters in the word, what is the probability of no letter 'u' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {y: 1, h: 2, d: 1}, shuffle the letters in the word, what is the probability of no letter 'd' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {j: 2, g: 1, s: 1}, shuffle the letters in the word, what is the probability of no letter 's' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {a: 1, y: 1, w: 2}, shuffle the letters in the word, what is the probability of no letter 'w' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {t: 1, m: 2, b: 1}, shuffle the letters in the word, what is the probability of no letter 't' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {q: 1, a: 2, y: 1}, shuffle the letters in the word, what is the probability of no letter 'y' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {z: 2, y: 1, l: 1}, shuffle the letters in the word, what is the probability of no letter 'z' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {g: 1, h: 1, m: 2}, shuffle the letters in the word, what is the probability of no letter 'h' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {p: 1, s: 2, n: 1}, shuffle the letters in the word, what is the probability of no letter 'p' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {q: 1, r: 2, o: 1}, shuffle the letters in the word, what is the probability of no letter 'o' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {u: 2, i: 1, h: 1}, shuffle the letters in the word, what is the probability of no letter 'h' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {w: 1, v: 2, k: 1}, shuffle the letters in the word, what is the probability of no letter 'v' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {b: 1, v: 2, y: 1}, shuffle the letters in the word, what is the probability of no letter 'y' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {t: 1, k: 1, y: 2}, shuffle the letters in the word, what is the probability of no letter 'y' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {m: 2, a: 1, k: 1}, shuffle the letters in the word, what is the probability of no letter 'k' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {n: 1, v: 1, f: 2}, shuffle the letters in the word, what is the probability of no letter 'v' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {d: 1, w: 2, f: 1}, shuffle the letters in the word, what is the probability of no letter 'w' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {j: 1, t: 1, k: 2}, shuffle the letters in the word, what is the probability of no letter 't' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {m: 1, g: 1, r: 2}, shuffle the letters in the word, what is the probability of no letter 'r' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {q: 1, z: 1, b: 2}, shuffle the letters in the word, what is the probability of no letter 'q' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {a: 2, h: 1, t: 1}, shuffle the letters in the word, what is the probability of no letter 't' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {v: 1, o: 2, d: 1}, shuffle the letters in the word, what is the probability of no letter 'v' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {y: 1, a: 2, f: 1}, shuffle the letters in the word, what is the probability of no letter 'y' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {d: 1, p: 2, f: 1}, shuffle the letters in the word, what is the probability of no letter 'f' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {q: 1, g: 1, x: 2}, shuffle the letters in the word, what is the probability of no letter 'q' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {o: 1, a: 2, d: 1}, shuffle the letters in the word, what is the probability of no letter 'o' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {r: 1, a: 2, h: 1}, shuffle the letters in the word, what is the probability of no letter 'a' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {r: 2, h: 1, s: 1}, shuffle the letters in the word, what is the probability of no letter 's' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {o: 2, m: 1, c: 1}, shuffle the letters in the word, what is the probability of no letter 'o' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {c: 2, m: 1, z: 1}, shuffle the letters in the word, what is the probability of no letter 'z' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {f: 2, j: 1, b: 1}, shuffle the letters in the word, what is the probability of no letter 'b' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {f: 2, y: 1, n: 1}, shuffle the letters in the word, what is the probability of no letter 'n' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {d: 2, t: 1, q: 1}, shuffle the letters in the word, what is the probability of no letter 't' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {v: 1, e: 1, i: 2}, shuffle the letters in the word, what is the probability of no letter 'e' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {y: 2, c: 1, z: 1}, shuffle the letters in the word, what is the probability of no letter 'y' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {k: 2, a: 1, v: 1}, shuffle the letters in the word, what is the probability of no letter 'v' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {f: 2, z: 1, h: 1}, shuffle the letters in the word, what is the probability of no letter 'z' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {e: 2, l: 1, p: 1}, shuffle the letters in the word, what is the probability of no letter 'l' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {m: 1, v: 2, l: 1}, shuffle the letters in the word, what is the probability of no letter 'm' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {l: 2, t: 1, d: 1}, shuffle the letters in the word, what is the probability of no letter 'd' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {d: 2, w: 1, c: 1}, shuffle the letters in the word, what is the probability of no letter 'w' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {h: 1, n: 1, i: 2}, shuffle the letters in the word, what is the probability of no letter 'h' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {m: 1, q: 2, u: 1}, shuffle the letters in the word, what is the probability of no letter 'm' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {m: 2, f: 1, v: 1}, shuffle the letters in the word, what is the probability of no letter 'v' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {e: 1, u: 1, a: 2}, shuffle the letters in the word, what is the probability of no letter 'a' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {y: 2, m: 1, j: 1}, shuffle the letters in the word, what is the probability of no letter 'j' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {i: 1, u: 2, v: 1}, shuffle the letters in the word, what is the probability of no letter 'v' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {a: 2, j: 1, x: 1}, shuffle the letters in the word, what is the probability of no letter 'x' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {g: 1, e: 2, h: 1}, shuffle the letters in the word, what is the probability of no letter 'h' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {d: 1, k: 2, w: 1}, shuffle the letters in the word, what is the probability of no letter 'k' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {p: 1, q: 2, l: 1}, shuffle the letters in the word, what is the probability of no letter 'l' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {s: 1, j: 1, b: 2}, shuffle the letters in the word, what is the probability of no letter 'b' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {d: 1, n: 2, t: 1}, shuffle the letters in the word, what is the probability of no letter 't' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {q: 2, y: 1, k: 1}, shuffle the letters in the word, what is the probability of no letter 'k' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {c: 1, p: 1, e: 2}, shuffle the letters in the word, what is the probability of no letter 'e' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {c: 1, s: 2, l: 1}, shuffle the letters in the word, what is the probability of no letter 'c' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {u: 1, b: 2, q: 1}, shuffle the letters in the word, what is the probability of no letter 'q' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {l: 1, j: 2, z: 1}, shuffle the letters in the word, what is the probability of no letter 'j' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {b: 1, e: 2, c: 1}, shuffle the letters in the word, what is the probability of no letter 'c' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {o: 1, b: 2, f: 1}, shuffle the letters in the word, what is the probability of no letter 'o' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {n: 1, f: 2, r: 1}, shuffle the letters in the word, what is the probability of no letter 'r' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {h: 2, k: 1, s: 1}, shuffle the letters in the word, what is the probability of no letter 's' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {h: 1, k: 1, e: 2}, shuffle the letters in the word, what is the probability of no letter 'e' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {t: 1, x: 1, f: 2}, shuffle the letters in the word, what is the probability of no letter 'f' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

3

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {l: 1, m: 2, s: 1}, shuffle the letters in the word, what is the probability of no letter 's' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {f: 1, n: 1, c: 2}, shuffle the letters in the word, what is the probability of no letter 'n' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {o: 2, r: 1, b: 1}, shuffle the letters in the word, what is the probability of no letter 'r' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {m: 2, k: 1, z: 1}, shuffle the letters in the word, what is the probability of no letter 'z' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {d: 2, b: 1, a: 1}, shuffle the letters in the word, what is the probability of no letter 'b' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]

7

MATH