messages listlengths 1 1 | ground_truth stringclasses 40 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {y: 2, h: 1, j: 2, o: 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 $\\fra... | 43 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {q: 1, i: 2, m: 1, b: 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 $\\fra... | 29 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {g: 1, a: 1, w: 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 $\\fra... | 37 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {w: 1, k: 3, 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... | 27 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {m: 3, f: 1, q: 1, t: 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 $\\fra... | 7 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {q: 2, b: 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... | 7 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {g: 1, i: 1, n: 2, 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 $\\fra... | 29 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {z: 4, k: 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... | 113 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {x: 2, q: 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... | 29 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {o: 1, n: 4, 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... | 113 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {s: 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 $\\frac{m}{n}$, wh... | 4 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {g: 3, c: 2, 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... | 29 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 2, e: 1, u: 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 $\\fra... | 25 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {w: 3, a: 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 $\\frac{m}{n}$, wh... | 9 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {a: 3, x: 1, g: 1, e: 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 $\\fra... | 59 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {c: 3, 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 $\\frac{m}{n}$, wh... | 13 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {x: 1, h: 1, e: 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... | 17 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {b: 1, t: 1, n: 2, s: 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 $\\fra... | 37 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {b: 2, y: 1, 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... | 17 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {w: 1, f: 1, 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... | 7 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {p: 1, c: 2, r: 2, t: 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 $\\fra... | 6 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {y: 5, 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 $\\frac{m}{n}$, wh... | 26 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {f: 1, p: 1, 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... | 27 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {u: 1, h: 2, y: 1, 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 $\\fra... | 6 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {f: 2, s: 3, v: 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... | 39 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {u: 3, w: 2, j: 1, 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 $\\fra... | 59 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {l: 5, 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 $\\frac{m}{n}$, wh... | 26 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {t: 2, d: 1, f: 2, 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 $\\fra... | 6 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {n: 1, v: 2, g: 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 $\\fra... | 43 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {a: 3, w: 1, g: 2, s: 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 $\\fra... | 59 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {t: 2, o: 1, l: 1, 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 $\\fra... | 29 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {q: 2, g: 1, 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... | 41 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {d: 1, w: 2, 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... | 7 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {j: 2, g: 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 $\\frac{m}{n}$, wh... | 19 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {v: 4, m: 1, e: 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... | 16 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {t: 2, h: 1, u: 2, i: 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 $\\fra... | 6 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {j: 2, o: 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 $\\frac{m}{n}$, wh... | 19 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {x: 1, q: 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... | 11 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {k: 2, z: 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... | 17 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {s: 1, e: 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... | 17 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {n: 1, m: 2, g: 1, 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 $\\fra... | 29 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {c: 2, r: 2, q: 1, o: 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 $\\fra... | 6 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {r: 1, c: 1, u: 1, z: 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 $\\fra... | 37 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {n: 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 $\\frac{m}{n}$, wh... | 13 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {q: 1, m: 1, y: 1, 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 $\\fra... | 3 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {g: 2, u: 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... | 39 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {s: 1, t: 1, v: 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... | 7 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {s: 1, m: 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... | 7 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {p: 3, z: 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... | 29 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {d: 1, e: 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 $\\frac{m}{n}$, wh... | 6 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {r: 4, 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 $\\frac{m}{n}$, wh... | 9 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {j: 1, r: 2, i: 1, e: 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 $\\fra... | 29 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {f: 1, x: 1, l: 2, 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 $\\fra... | 37 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {e: 2, z: 1, q: 1, g: 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 $\\fra... | 37 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {v: 1, c: 2, e: 1, 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 $\\fra... | 29 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {u: 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 $\\frac{m}{n}$, wh... | 13 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {x: 3, p: 1, k: 1, 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 $\\fra... | 59 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {i: 1, v: 1, s: 2, l: 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 $\\fra... | 37 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {b: 1, n: 4, 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... | 16 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {l: 1, e: 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... | 41 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {y: 2, 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 $\\frac{m}{n}$, wh... | 4 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {i: 3, 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 $\\frac{m}{n}$, wh... | 13 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {o: 3, v: 1, 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... | 11 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {s: 1, n: 1, q: 1, i: 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 $\\fra... | 4 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {n: 3, 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 $\\frac{m}{n}$, wh... | 13 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {i: 1, r: 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... | 17 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {j: 1, n: 3, r: 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... | 41 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {z: 2, q: 2, a: 1, 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 $\\fra... | 43 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {a: 1, f: 1, x: 1, o: 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 $\\fra... | 4 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {d: 1, g: 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... | 41 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {l: 1, v: 1, x: 1, 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 $\\fra... | 29 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {f: 3, u: 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 $\\frac{m}{n}$, wh... | 9 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {l: 1, c: 1, i: 2, s: 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 $\\fra... | 6 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 1, h: 2, q: 1, 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 $\\fra... | 122 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {e: 2, y: 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... | 11 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {t: 1, d: 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... | 7 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {h: 2, w: 5}, 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 $\\frac{m}{n}$, wh... | 26 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {t: 1, s: 2, o: 2, 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 $\\fra... | 43 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {v: 2, g: 1, 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... | 11 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {p: 2, d: 2, h: 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... | 7 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {b: 1, w: 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... | 27 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {l: 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 $\\frac{m}{n}$, wh... | 13 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {i: 1, n: 1, j: 2, b: 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 $\\fra... | 37 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {b: 1, s: 1, i: 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... | 27 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {q: 1, g: 1, y: 2, b: 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 $\\fra... | 37 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {l: 1, r: 1, n: 2, c: 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 $\\fra... | 29 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {k: 4, 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 $\\frac{m}{n}$, wh... | 9 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {k: 1, q: 1, a: 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 $\\fra... | 29 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {h: 3, 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 $\\frac{m}{n}$, wh... | 13 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {g: 4, n: 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 $\\frac{m}{n}$, wh... | 9 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {o: 1, s: 1, p: 2, 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 $\\fra... | 37 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {g: 2, c: 1, e: 3, u: 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 $\\fra... | 122 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {g: 1, o: 2, b: 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... | 17 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {l: 3, 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 $\\frac{m}{n}$, wh... | 13 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {h: 2, t: 1, 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... | 7 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {r: 2, u: 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 $\\frac{m}{n}$, wh... | 19 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {u: 3, t: 1, 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... | 11 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {d: 2, p: 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... | 39 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {z: 1, o: 5}, 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 $\\frac{m}{n}$, wh... | 7 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {c: 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 $\\frac{m}{n}$, wh... | 4 | MATH |
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