messages listlengths 1 1 | ground_truth stringclasses 61
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {z: 4, h: 2, x: 1, u: 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 $\\fra... | 67 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {f: 5, i: 5}, 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 $\\frac{m}{n}$, wh... | 317 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {q: 4, c: 3, x: 3}, shuffle the letters in the word, what is the probability of exact 2 letter 'q' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n... | 81 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {p: 2, w: 2, b: 3, c: 3}, shuffle the letters in the word, what is the probability of exact 3 letter 'b' remains in the same position?\nIf the probability can be written as the form $\\fra... | 121 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {a: 6, i: 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 $\\frac{m}{n}$, wh... | 5 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {o: 4, i: 2, c: 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... | 25 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {q: 3, g: 2, s: 3}, shuffle the letters in the word, what is the probability of exact 3 letter 'q' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n... | 57 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {t: 6, b: 2, o: 1}, shuffle the letters in the word, what is the probability of exact 2 letter 't' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n... | 109 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {b: 2, f: 1, p: 5}, 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... | 29 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {y: 2, k: 4, n: 1, i: 3}, 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 $\\fra... | 11 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {b: 4, l: 2, g: 1, z: 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 $\\fra... | 10 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {d: 3, x: 2, a: 3}, shuffle the letters in the word, what is the probability of exact 2 letter 'x' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n... | 29 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {r: 4, e: 4}, 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 $\\frac{m}{n}$, wh... | 37 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {b: 3, u: 2, m: 2, k: 1}, 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 $\\fra... | 29 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {q: 1, j: 3, c: 2, g: 3}, 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 $\\fra... | 10 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {a: 1, b: 2, e: 2, o: 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 $\\fra... | 9 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {r: 2, j: 1, f: 4, c: 1}, 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 $\\fra... | 13 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {g: 5, l: 3}, 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 $\\frac{m}{n}$, wh... | 57 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {u: 1, o: 5, a: 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... | 23 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {h: 3, t: 3, o: 2, f: 2}, 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 $\\fra... | 46 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {z: 2, g: 1, q: 4, 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 $\\fra... | 9 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {i: 2, o: 2, y: 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... | 9 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {k: 3, l: 1, x: 1, r: 3}, 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 $\\fra... | 9 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {e: 4, s: 3, j: 2}, 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... | 23 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {v: 3, a: 2, m: 2, i: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'v' remains in the same position?\nIf the probability can be written as the form $\\fra... | 39 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {u: 4, c: 1, o: 2, f: 2}, 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 $\\fra... | 10 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {r: 5, y: 3, v: 1}, 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... | 83 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {j: 1, d: 2, t: 1, r: 6}, 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 $\\fra... | 55 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {a: 4, p: 6}, 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 $\\frac{m}{n}$, wh... | 46 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {z: 4, w: 3, n: 2}, 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... | 89 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {u: 6, v: 4}, shuffle the letters in the word, what is the probability of exact 1 letter 'v' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$, wh... | 59 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {m: 3, h: 2, a: 5}, 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... | 89 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {d: 7, s: 3}, 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 $\\frac{m}{n}$, wh... | 11 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {w: 4, r: 4}, 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 $\\frac{m}{n}$, wh... | 7 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {i: 5, n: 4}, shuffle the letters in the word, what is the probability of exact 2 letter 'i' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$, wh... | 83 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {a: 3, y: 4, b: 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... | 85 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {z: 3, v: 2, d: 3}, 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... | 29 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {x: 3, c: 2, m: 4}, 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... | 37 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {k: 4, u: 2, p: 2}, 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... | 29 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {g: 3, z: 2, t: 2, p: 1}, 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 $\\fra... | 39 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {p: 4, d: 6}, shuffle the letters in the word, what is the probability of exact 1 letter 'd' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$, wh... | 271 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {d: 4, i: 4, c: 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... | 10 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {r: 3, d: 2, t: 3, f: 1}, 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 $\\fra... | 23 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {m: 5, w: 1, k: 1, q: 3}, 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 $\\fra... | 347 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {k: 1, o: 2, g: 2, h: 4}, 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 $\\fra... | 5 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {w: 4, x: 4}, shuffle the letters in the word, what is the probability of exact 1 letter 'x' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$, wh... | 7 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {z: 3, v: 4, x: 3}, 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... | 53 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {t: 4, 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 $\\frac{m}{n}$, wh... | 44 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {s: 2, a: 2, p: 6}, 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... | 11 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {y: 3, d: 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 $\\frac{m}{n}$, wh... | 85 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {e: 6, b: 4}, shuffle the letters in the word, what is the probability of exact 3 letter 'b' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$, wh... | 73 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {w: 3, e: 5}, shuffle the letters in the word, what is the probability of exact 3 letter 'w' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$, wh... | 57 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {u: 2, y: 3, a: 2, x: 1}, 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 $\\fra... | 37 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {j: 3, m: 4, 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... | 43 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {s: 4, g: 3, i: 3}, 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... | 29 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {s: 3, d: 2, r: 3, q: 2}, shuffle the letters in the word, what is the probability of exact 2 letter 'q' remains in the same position?\nIf the probability can be written as the form $\\fra... | 46 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {t: 4, j: 5}, shuffle the letters in the word, what is the probability of exact 3 letter 'j' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$, wh... | 74 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {a: 6, m: 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 $\\frac{m}{n}$, wh... | 17 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {x: 3, e: 6}, 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 $\\frac{m}{n}$, wh... | 47 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {q: 2, h: 4, g: 1, k: 3}, shuffle the letters in the word, what is the probability of exact 1 letter 'k' remains in the same position?\nIf the probability can be written as the form $\\fra... | 53 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {y: 2, e: 5, c: 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... | 37 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {n: 2, d: 3, s: 4}, 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... | 23 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {w: 3, q: 3, f: 2, l: 2}, shuffle the letters in the word, what is the probability of exact 3 letter 'w' remains in the same position?\nIf the probability can be written as the form $\\fra... | 121 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {i: 5, r: 1, m: 3}, 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... | 10 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {c: 1, g: 2, a: 2, f: 4}, 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 $\\fra... | 10 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {r: 3, g: 2, s: 4}, shuffle the letters in the word, what is the probability of exact 3 letter 's' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n... | 131 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {b: 4, n: 6}, 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 $\\frac{m}{n}$, wh... | 23 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {u: 5, a: 4}, 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 $\\frac{m}{n}$, wh... | 68 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {h: 5, t: 2, d: 2}, 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... | 37 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {u: 2, g: 4, h: 1, i: 1}, 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 $\\fra... | 9 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {n: 3, l: 2, b: 1, c: 3}, 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 $\\fra... | 47 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {h: 3, t: 2, u: 2, e: 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 $\\fra... | 9 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {r: 2, a: 2, s: 4, p: 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 $\\fra... | 11 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {y: 2, v: 1, x: 5, k: 2}, shuffle the letters in the word, what is the probability of exact 1 letter 'k' remains in the same position?\nIf the probability can be written as the form $\\fra... | 11 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {s: 3, d: 1, h: 1, f: 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 $\\fra... | 11 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {v: 1, p: 4, z: 3}, 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... | 39 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {i: 2, k: 6}, shuffle the letters in the word, what is the probability of exact 1 letter 'k' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$, wh... | 31 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {w: 3, d: 3, x: 1, h: 2}, shuffle the letters in the word, what is the probability of exact 2 letter 'h' remains in the same position?\nIf the probability can be written as the form $\\fra... | 37 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {l: 4, k: 4, e: 2}, 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... | 73 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {i: 5, t: 1, c: 2, g: 2}, 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 $\\fra... | 56 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {d: 4, p: 3, k: 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... | 47 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {u: 5, n: 2, a: 1, c: 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 $\\fra... | 10 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {n: 4, x: 1, 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... | 88 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {f: 3, r: 3, o: 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... | 85 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {r: 4, j: 3, k: 3}, 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... | 43 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {k: 2, h: 2, q: 2, t: 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 $\\fra... | 56 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {t: 4, b: 6}, shuffle the letters in the word, what is the probability of exact 2 letter 't' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$, wh... | 81 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {z: 4, t: 5}, shuffle the letters in the word, what is the probability of exact 2 letter 't' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n}$, wh... | 83 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {d: 3, s: 2, l: 1, x: 2}, 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 $\\fra... | 29 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {i: 3, n: 2, o: 3, h: 2}, 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 $\\fra... | 121 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {u: 3, i: 1, t: 1, d: 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 $\\fra... | 10 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {k: 5, x: 2, a: 2}, shuffle the letters in the word, what is the probability of exact 2 letter 'a' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n... | 37 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {c: 4, l: 2, u: 1, y: 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 $\\fra... | 23 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {g: 2, p: 2, c: 6}, shuffle the letters in the word, what is the probability of exact 2 letter 'g' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n... | 46 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {p: 1, q: 2, d: 5}, 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... | 75 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {s: 4, y: 5}, 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 $\\frac{m}{n}$, wh... | 74 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {y: 4, a: 2, o: 3, m: 1}, 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 $\\fra... | 81 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {j: 3, z: 2, y: 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... | 65 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {f: 5, x: 2, u: 3}, shuffle the letters in the word, what is the probability of exact 1 letter 'f' remains in the same position?\nIf the probability can be written as the form $\\frac{m}{n... | 347 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 5 letters from the multiset {d: 2, r: 1, b: 3, i: 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 $\\fra... | 9 | MATH |
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