sunyiyou/math_combinatory_probability_no_fixed_points_level_2

messages listlengths 1 1	ground_truth stringclasses 3 values	dataset stringclasses 1 value
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {l: 3, c: 2, v: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {b: 2, e: 2, l: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	17	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {k: 1, w: 3, u: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {r: 4, m: 1, x: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	16	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {b: 2, i: 1, k: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {x: 1, y: 1, c: 4}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	16	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {m: 1, k: 2, f: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 2, x: 2, j: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	17	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {z: 2, n: 1, f: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {p: 1, s: 3, n: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {u: 2, q: 1, g: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {i: 1, l: 4, j: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	16	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {z: 2, i: 2, f: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	17	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {h: 3, g: 1, o: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {i: 1, w: 2, o: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {m: 2, k: 1, b: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {u: 2, i: 1, b: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {p: 2, o: 2, h: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	17	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {k: 1, a: 2, y: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {i: 2, z: 1, r: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {t: 2, x: 1, l: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {c: 1, a: 4, n: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	16	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {x: 2, m: 3, d: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {f: 1, i: 3, h: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {x: 2, u: 2, q: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	17	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {c: 1, b: 2, h: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {f: 1, r: 2, j: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {o: 1, z: 3, w: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {t: 1, x: 1, n: 4}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	16	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {o: 1, q: 2, m: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {p: 2, d: 2, k: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	17	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {p: 2, k: 2, c: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	17	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {g: 3, d: 1, f: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {g: 1, x: 1, t: 4}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	16	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {i: 1, a: 1, t: 4}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	16	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {d: 1, t: 3, p: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {l: 3, r: 2, p: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {m: 2, o: 1, g: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {t: 3, k: 2, m: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {x: 3, r: 1, d: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {m: 1, n: 2, v: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 2, u: 2, p: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	17	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {d: 2, n: 3, r: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {w: 2, m: 1, h: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {j: 1, q: 3, k: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {w: 3, e: 2, x: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {y: 2, w: 1, l: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {d: 2, j: 1, u: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {v: 1, t: 2, j: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {c: 1, t: 2, a: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {t: 4, a: 1, y: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	16	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {h: 2, l: 2, j: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	17	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {c: 3, j: 1, w: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {o: 2, h: 2, c: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	17	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {k: 3, o: 1, l: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {o: 3, p: 2, n: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {i: 2, b: 2, o: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	17	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {b: 3, c: 1, a: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {t: 2, n: 1, f: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {q: 1, t: 3, f: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {g: 1, d: 2, w: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {h: 3, c: 1, p: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {q: 2, x: 3, z: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {f: 1, n: 2, e: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {y: 1, a: 3, g: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {j: 2, y: 2, a: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	17	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 3, h: 2, q: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 2, s: 2, t: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	17	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {f: 3, w: 1, j: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {t: 1, x: 3, o: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {a: 2, k: 3, r: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {h: 2, n: 3, p: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {w: 4, c: 1, k: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	16	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {c: 2, h: 2, w: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	17	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {d: 1, s: 1, j: 4}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	16	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {k: 3, c: 2, f: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 2, v: 2, m: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	17	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {e: 2, s: 2, a: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	17	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {s: 2, m: 2, y: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	17	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {o: 3, j: 1, x: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {t: 1, j: 3, i: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {q: 2, k: 2, b: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	17	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {p: 1, r: 3, a: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {o: 3, q: 1, p: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 2, y: 3, a: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {t: 3, r: 2, q: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {a: 2, c: 2, h: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	17	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {r: 2, v: 2, u: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	17	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {b: 3, a: 2, m: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 2, j: 2, i: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	17	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {y: 1, t: 3, x: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {d: 2, j: 3, k: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 2, j: 2, u: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	17	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {e: 3, k: 2, q: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {a: 2, f: 3, k: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {f: 1, h: 3, x: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {h: 2, v: 2, c: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	17	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {l: 2, g: 1, d: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {y: 2, r: 2, j: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	17	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {d: 1, u: 3, a: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]	11	MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {l: 3, c: 2, v: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {b: 2, e: 2, l: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

17

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {k: 1, w: 3, u: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {r: 4, m: 1, x: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

16

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {b: 2, i: 1, k: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {x: 1, y: 1, c: 4}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

16

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {m: 1, k: 2, f: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 2, x: 2, j: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

17

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {z: 2, n: 1, f: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {p: 1, s: 3, n: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {u: 2, q: 1, g: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {i: 1, l: 4, j: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

16

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {z: 2, i: 2, f: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

17

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {h: 3, g: 1, o: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {i: 1, w: 2, o: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {m: 2, k: 1, b: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {u: 2, i: 1, b: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {p: 2, o: 2, h: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

17

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {k: 1, a: 2, y: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {i: 2, z: 1, r: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {t: 2, x: 1, l: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {c: 1, a: 4, n: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

16

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {x: 2, m: 3, d: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {f: 1, i: 3, h: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {x: 2, u: 2, q: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

17

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {c: 1, b: 2, h: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {f: 1, r: 2, j: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {o: 1, z: 3, w: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {t: 1, x: 1, n: 4}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

16

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {o: 1, q: 2, m: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {p: 2, d: 2, k: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

17

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {p: 2, k: 2, c: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

17

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {g: 3, d: 1, f: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {g: 1, x: 1, t: 4}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

16

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {i: 1, a: 1, t: 4}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

16

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {d: 1, t: 3, p: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {l: 3, r: 2, p: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {m: 2, o: 1, g: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {t: 3, k: 2, m: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {x: 3, r: 1, d: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {m: 1, n: 2, v: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 2, u: 2, p: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

17

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {d: 2, n: 3, r: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {w: 2, m: 1, h: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {j: 1, q: 3, k: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {w: 3, e: 2, x: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {y: 2, w: 1, l: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {d: 2, j: 1, u: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {v: 1, t: 2, j: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {c: 1, t: 2, a: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {t: 4, a: 1, y: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

16

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {h: 2, l: 2, j: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

17

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {c: 3, j: 1, w: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {o: 2, h: 2, c: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

17

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {k: 3, o: 1, l: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {o: 3, p: 2, n: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {i: 2, b: 2, o: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

17

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {b: 3, c: 1, a: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {t: 2, n: 1, f: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {q: 1, t: 3, f: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {g: 1, d: 2, w: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {h: 3, c: 1, p: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {q: 2, x: 3, z: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {f: 1, n: 2, e: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {y: 1, a: 3, g: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {j: 2, y: 2, a: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

17

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 3, h: 2, q: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 2, s: 2, t: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

17

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {f: 3, w: 1, j: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {t: 1, x: 3, o: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {a: 2, k: 3, r: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {h: 2, n: 3, p: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {w: 4, c: 1, k: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

16

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {c: 2, h: 2, w: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

17

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {d: 1, s: 1, j: 4}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

16

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {k: 3, c: 2, f: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 2, v: 2, m: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

17

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {e: 2, s: 2, a: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

17

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {s: 2, m: 2, y: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

17

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {o: 3, j: 1, x: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {t: 1, j: 3, i: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {q: 2, k: 2, b: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

17

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {p: 1, r: 3, a: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {o: 3, q: 1, p: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 2, y: 3, a: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {t: 3, r: 2, q: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {a: 2, c: 2, h: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

17

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {r: 2, v: 2, u: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

17

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {b: 3, a: 2, m: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 2, j: 2, i: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

17

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {y: 1, t: 3, x: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {d: 2, j: 3, k: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 2, j: 2, u: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

17

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {e: 3, k: 2, q: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {a: 2, f: 3, k: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {f: 1, h: 3, x: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {h: 2, v: 2, c: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

17

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {l: 2, g: 1, d: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {y: 2, r: 2, j: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

17

MATH

[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {d: 1, u: 3, a: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\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" } ]

11

MATH