| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {v: 3, u: 1, o: 3}, shuffle the letters in the word, what is the probability of exact 1 letter 'o' remains in the same 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"}], "ground_truth": "7", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {h: 1, l: 1, d: 6}, shuffle the letters in the word, what is the probability of exact 1 letter 'h' remains in the same 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"}], "ground_truth": "9", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {m: 3, y: 3}, shuffle the letters in the word, what is the probability of exact 2 letter 'm' remains in the same 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"}], "ground_truth": "23", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {d: 4, t: 2}, shuffle the letters in the word, what is the probability of exact 3 letter 'd' remains in the same 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"}], "ground_truth": "6", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {h: 4, x: 5}, shuffle the letters in the word, what is the probability of exact 1 letter 'h' remains in the same 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"}], "ground_truth": "88", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {t: 1, p: 2, k: 3, l: 2}, shuffle the letters in the word, what is the probability of exact 1 letter 'p' remains in the same 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"}], "ground_truth": "9", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {k: 6, e: 3}, shuffle the letters in the word, what is the probability of exact 3 letter 'e' remains in the same 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"}], "ground_truth": "85", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {u: 2, g: 3, p: 1, j: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'p' remains in the same 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"}], "ground_truth": "8", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {s: 4, q: 1, m: 2, t: 1}, shuffle the letters in the word, what is the probability of exact 2 letter 's' remains in the same 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"}], "ground_truth": "8", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {s: 1, j: 3, h: 1, k: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 's' remains in the same 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"}], "ground_truth": "7", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {r: 3, g: 2, c: 3}, shuffle the letters in the word, what is the probability of exact 1 letter 'g' remains in the same 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"}], "ground_truth": "9", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {e: 3, v: 1, m: 2, n: 2}, shuffle the letters in the word, what is the probability of exact 2 letter 'm' remains in the same 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"}], "ground_truth": "29", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {o: 4, w: 3}, shuffle the letters in the word, what is the probability of exact 3 letter 'o' remains in the same 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"}], "ground_truth": "39", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {u: 5, w: 2, l: 2}, shuffle the letters in the word, what is the probability of exact 3 letter 'u' remains in the same 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"}], "ground_truth": "68", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {p: 4, h: 2, w: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'h' remains in the same 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"}], "ground_truth": "4", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {y: 3, l: 3, f: 1, o: 1}, shuffle the letters in the word, what is the probability of exact 3 letter 'y' remains in the same 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"}], "ground_truth": "57", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {m: 5, s: 3}, shuffle the letters in the word, what is the probability of exact 3 letter 'm' remains in the same 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"}], "ground_truth": "33", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {e: 4, r: 3, g: 2}, shuffle the letters in the word, what is the probability of exact 1 letter 'g' remains in the same 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"}], "ground_truth": "5", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {n: 2, q: 6}, shuffle the letters in the word, what is the probability of exact 2 letter 'n' remains in the same 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"}], "ground_truth": "29", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {b: 1, p: 1, u: 2, o: 2}, shuffle the letters in the word, what is the probability of exact 2 letter 'o' remains in the same 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"}], "ground_truth": "16", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {y: 1, o: 3, c: 1, z: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'z' remains in the same 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"}], "ground_truth": "7", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {e: 3, u: 5}, shuffle the letters in the word, what is the probability of exact 2 letter 'u' remains in the same 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"}], "ground_truth": "39", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {h: 3, o: 2, l: 2, r: 2}, shuffle the letters in the word, what is the probability of exact 1 letter 'r' remains in the same 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"}], "ground_truth": "5", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {o: 1, n: 3, y: 1, z: 2}, shuffle the letters in the word, what is the probability of exact 1 letter 'y' remains in the same 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"}], "ground_truth": "8", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {i: 4, w: 3}, shuffle the letters in the word, what is the probability of exact 3 letter 'i' remains in the same 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"}], "ground_truth": "38", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {c: 1, a: 2, i: 3, y: 2}, shuffle the letters in the word, what is the probability of exact 1 letter 'y' remains in the same 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"}], "ground_truth": "9", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {z: 3, o: 3}, shuffle the letters in the word, what is the probability of exact 2 letter 'z' remains in the same 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"}], "ground_truth": "23", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {r: 1, g: 2, x: 2, f: 3}, shuffle the letters in the word, what is the probability of exact 3 letter 'f' remains in the same 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"}], "ground_truth": "57", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {z: 2, t: 1, q: 1, d: 3}, shuffle the letters in the word, what is the probability of exact 2 letter 'd' remains in the same 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"}], "ground_truth": "41", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {j: 2, q: 4}, shuffle the letters in the word, what is the probability of exact 1 letter 'q' remains in the same 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"}], "ground_truth": "22", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {h: 3, l: 2, b: 2}, shuffle the letters in the word, what is the probability of exact 1 letter 'l' remains in the same 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"}], "ground_truth": "9", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {p: 2, o: 2, f: 1, w: 2}, shuffle the letters in the word, what is the probability of exact 1 letter 'o' remains in the same 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"}], "ground_truth": "4", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {y: 5, j: 3}, shuffle the letters in the word, what is the probability of exact 3 letter 'y' remains in the same 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"}], "ground_truth": "31", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {t: 2, y: 4}, shuffle the letters in the word, what is the probability of exact 2 letter 'y' remains in the same 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"}], "ground_truth": "6", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {b: 2, f: 5}, shuffle the letters in the word, what is the probability of exact 1 letter 'b' remains in the same 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"}], "ground_truth": "9", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {l: 3, w: 2, y: 2, k: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'w' remains in the same 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"}], "ground_truth": "5", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {k: 2, c: 1, v: 3, m: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'c' remains in the same 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"}], "ground_truth": "8", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {u: 5, o: 4}, shuffle the letters in the word, what is the probability of exact 1 letter 'u' remains in the same 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"}], "ground_truth": "19", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {b: 4, v: 4}, shuffle the letters in the word, what is the probability of exact 2 letter 'b' remains in the same 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"}], "ground_truth": "44", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {f: 1, v: 3, b: 4}, shuffle the letters in the word, what is the probability of exact 1 letter 'b' remains in the same 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"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {v: 6, r: 4}, shuffle the letters in the word, what is the probability of exact 1 letter 'r' remains in the same 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"}], "ground_truth": "59", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {h: 4, z: 3, r: 3}, shuffle the letters in the word, what is the probability of exact 2 letter 'z' remains in the same 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"}], "ground_truth": "43", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {y: 3, l: 5}, shuffle the letters in the word, what is the probability of exact 2 letter 'y' remains in the same 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"}], "ground_truth": "9", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {h: 4, e: 3, i: 2, z: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'z' remains in the same 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"}], "ground_truth": "11", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {w: 2, a: 1, z: 3, r: 2}, shuffle the letters in the word, what is the probability of exact 3 letter 'z' remains in the same 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"}], "ground_truth": "57", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {q: 2, a: 4, c: 2}, shuffle the letters in the word, what is the probability of exact 3 letter 'a' remains in the same 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"}], "ground_truth": "37", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {y: 3, t: 6}, shuffle the letters in the word, what is the probability of exact 3 letter 'y' remains in the same 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"}], "ground_truth": "85", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {n: 5, v: 5}, shuffle the letters in the word, what is the probability of exact 2 letter 'v' remains in the same 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"}], "ground_truth": "317", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {e: 2, q: 6}, shuffle the letters in the word, what is the probability of exact 1 letter 'q' remains in the same 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"}], "ground_truth": "31", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {e: 2, l: 4, w: 1, v: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'w' remains in the same 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"}], "ground_truth": "9", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {y: 1, a: 4, d: 4}, shuffle the letters in the word, what is the probability of exact 1 letter 'y' remains in the same 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"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {j: 3, e: 5}, shuffle the letters in the word, what is the probability of exact 2 letter 'j' remains in the same 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"}], "ground_truth": "65", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {u: 1, s: 3, a: 2, e: 3}, shuffle the letters in the word, what is the probability of exact 1 letter 'a' remains in the same 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"}], "ground_truth": "5", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {b: 3, u: 2, f: 3, t: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 't' remains in the same 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"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {t: 7, m: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'm' remains in the same 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"}], "ground_truth": "9", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {x: 2, y: 3, u: 3}, shuffle the letters in the word, what is the probability of exact 1 letter 'u' remains in the same 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"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {x: 3, l: 5}, shuffle the letters in the word, what is the probability of exact 3 letter 'l' remains in the same 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"}], "ground_truth": "31", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {j: 5, q: 3}, shuffle the letters in the word, what is the probability of exact 2 letter 'j' remains in the same 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"}], "ground_truth": "75", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {g: 5, i: 4}, shuffle the letters in the word, what is the probability of exact 1 letter 'g' remains in the same 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"}], "ground_truth": "169", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {f: 4, t: 6}, shuffle the letters in the word, what is the probability of exact 1 letter 't' remains in the same 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"}], "ground_truth": "46", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {q: 2, t: 1, j: 4, r: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'q' remains in the same 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"}], "ground_truth": "37", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {g: 3, y: 5}, shuffle the letters in the word, what is the probability of exact 2 letter 'y' remains in the same 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"}], "ground_truth": "39", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {i: 4, h: 6}, shuffle the letters in the word, what is the probability of exact 1 letter 'h' remains in the same 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"}], "ground_truth": "46", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {y: 6, b: 3}, shuffle the letters in the word, what is the probability of exact 2 letter 'y' remains in the same 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"}], "ground_truth": "109", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {b: 4, m: 1, c: 3, h: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'b' remains in the same 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"}], "ground_truth": "88", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {z: 3, m: 3, u: 2}, shuffle the letters in the word, what is the probability of exact 1 letter 'u' remains in the same 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"}], "ground_truth": "9", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {c: 4, f: 5}, shuffle the letters in the word, what is the probability of exact 2 letter 'c' remains in the same 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"}], "ground_truth": "26", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {d: 4, m: 5}, shuffle the letters in the word, what is the probability of exact 1 letter 'm' remains in the same 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"}], "ground_truth": "19", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {w: 3, b: 2, r: 1, n: 2}, shuffle the letters in the word, what is the probability of exact 1 letter 'n' remains in the same 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"}], "ground_truth": "9", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {s: 4, n: 6}, shuffle the letters in the word, what is the probability of exact 2 letter 's' remains in the same 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"}], "ground_truth": "81", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {f: 5, c: 3}, shuffle the letters in the word, what is the probability of exact 3 letter 'c' remains in the same 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"}], "ground_truth": "57", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {o: 4, i: 2, p: 2, t: 2}, shuffle the letters in the word, what is the probability of exact 2 letter 'o' remains in the same 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"}], "ground_truth": "25", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {i: 1, s: 4, z: 4}, shuffle the letters in the word, what is the probability of exact 1 letter 'i' remains in the same 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"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {q: 6, o: 4}, shuffle the letters in the word, what is the probability of exact 2 letter 'o' remains in the same 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"}], "ground_truth": "25", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {t: 4, x: 1, f: 4}, shuffle the letters in the word, what is the probability of exact 2 letter 'f' remains in the same 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"}], "ground_truth": "26", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {m: 3, l: 3, d: 2, n: 1}, shuffle the letters in the word, what is the probability of exact 3 letter 'm' remains in the same 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"}], "ground_truth": "85", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {m: 5, l: 3, u: 2}, shuffle the letters in the word, what is the probability of exact 3 letter 'm' remains in the same 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"}], "ground_truth": "89", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {a: 2, c: 5, y: 2}, shuffle the letters in the word, what is the probability of exact 2 letter 'y' remains in the same 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"}], "ground_truth": "37", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {v: 2, d: 3, c: 2, r: 3}, shuffle the letters in the word, what is the probability of exact 3 letter 'r' remains in the same 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"}], "ground_truth": "121", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {k: 2, q: 8}, shuffle the letters in the word, what is the probability of exact 2 letter 'k' remains in the same 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"}], "ground_truth": "46", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {d: 8, p: 2}, shuffle the letters in the word, what is the probability of exact 2 letter 'p' remains in the same 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"}], "ground_truth": "46", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {d: 2, r: 8}, shuffle the letters in the word, what is the probability of exact 2 letter 'r' remains in the same 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"}], "ground_truth": "17", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {o: 4, j: 3, f: 3}, shuffle the letters in the word, what is the probability of exact 2 letter 'j' remains in the same 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"}], "ground_truth": "131", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {v: 5, d: 3}, shuffle the letters in the word, what is the probability of exact 3 letter 'v' remains in the same 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"}], "ground_truth": "71", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {z: 5, e: 3}, shuffle the letters in the word, what is the probability of exact 1 letter 'e' remains in the same 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"}], "ground_truth": "39", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {b: 2, g: 3, i: 3, n: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'b' remains in the same 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"}], "ground_truth": "23", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {m: 2, y: 3, q: 2, w: 2}, shuffle the letters in the word, what is the probability of exact 1 letter 'q' remains in the same 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"}], "ground_truth": "23", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {n: 4, w: 4}, shuffle the letters in the word, what is the probability of exact 3 letter 'n' remains in the same 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"}], "ground_truth": "37", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {r: 1, e: 5, c: 4}, shuffle the letters in the word, what is the probability of exact 1 letter 'r' remains in the same 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"}], "ground_truth": "11", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {h: 4, p: 4}, shuffle the letters in the word, what is the probability of exact 1 letter 'h' remains in the same 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"}], "ground_truth": "7", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {r: 1, e: 4, g: 1, z: 3}, shuffle the letters in the word, what is the probability of exact 2 letter 'z' remains in the same 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"}], "ground_truth": "47", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {b: 2, c: 3, j: 2, r: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'b' remains in the same 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"}], "ground_truth": "9", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {k: 1, x: 2, r: 2, f: 3}, shuffle the letters in the word, what is the probability of exact 2 letter 'r' remains in the same 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"}], "ground_truth": "29", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {n: 3, p: 3, a: 3}, shuffle the letters in the word, what is the probability of exact 3 letter 'a' remains in the same 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"}], "ground_truth": "85", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {h: 2, e: 3, i: 2, r: 3}, shuffle the letters in the word, what is the probability of exact 1 letter 'i' remains in the same 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"}], "ground_truth": "11", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {t: 4, r: 2, d: 4}, shuffle the letters in the word, what is the probability of exact 1 letter 'r' remains in the same 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"}], "ground_truth": "11", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {m: 3, h: 2, s: 3}, shuffle the letters in the word, what is the probability of exact 2 letter 's' remains in the same 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"}], "ground_truth": "65", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {k: 5, b: 3}, shuffle the letters in the word, what is the probability of exact 2 letter 'b' remains in the same 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"}], "ground_truth": "65", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {m: 3, c: 1, u: 3, s: 3}, shuffle the letters in the word, what is the probability of exact 3 letter 'u' remains in the same 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"}], "ground_truth": "121", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {s: 3, v: 5, q: 1}, shuffle the letters in the word, what is the probability of exact 2 letter 'v' remains in the same 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"}], "ground_truth": "83", "dataset": "MATH"} | |