messages listlengths 1 1 | ground_truth stringclasses 43 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {u: 2, b: 4, d: 3}, shuffle the letters in the word, what is the probability of no letter 'u' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 7 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {v: 2, s: 2, z: 1, y: 1}, shuffle the letters in the word, what is the probability of no letter 'z' occupy any of their original positions?\nIf the probability can be written as the form $... | 11 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {z: 2, j: 6}, shuffle the letters in the word, what is the probability of no letter 'j' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 29 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {r: 4, p: 3, t: 1}, shuffle the letters in the word, what is the probability of no letter 'r' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 89 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 3, p: 2, q: 2}, shuffle the letters in the word, what is the probability of no letter 'n' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 51 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {o: 2, l: 2, u: 1, r: 2}, shuffle the letters in the word, what is the probability of no letter 'r' occupy any of their original positions?\nIf the probability can be written as the form $... | 5 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {x: 4, i: 3}, shuffle the letters in the word, what is the probability of no letter 'x' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 44 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {f: 3, h: 1, o: 1, r: 3}, shuffle the letters in the word, what is the probability of no letter 'o' occupy any of their original positions?\nIf the probability can be written as the form $... | 15 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {w: 4, x: 1, n: 1, b: 3}, shuffle the letters in the word, what is the probability of no letter 'n' occupy any of their original positions?\nIf the probability can be written as the form $... | 17 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {a: 1, w: 3, l: 1, j: 1}, shuffle the letters in the word, what is the probability of no letter 'j' occupy any of their original positions?\nIf the probability can be written as the form $... | 11 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {a: 5, n: 4}, shuffle the letters in the word, what is the probability of no letter 'a' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 9 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {f: 2, m: 1, i: 1, j: 2}, shuffle the letters in the word, what is the probability of no letter 'f' occupy any of their original positions?\nIf the probability can be written as the form $... | 23 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {w: 4, c: 4}, shuffle the letters in the word, what is the probability of no letter 'w' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 19 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {a: 2, d: 3, k: 2}, shuffle the letters in the word, what is the probability of no letter 'k' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 34 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {z: 3, v: 4, a: 2}, shuffle the letters in the word, what is the probability of no letter 'v' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 181 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {i: 2, c: 3, f: 2}, shuffle the letters in the word, what is the probability of no letter 'c' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 51 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {y: 3, i: 3, w: 3}, shuffle the letters in the word, what is the probability of no letter 'i' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 67 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {k: 1, x: 1, l: 2, y: 3}, shuffle the letters in the word, what is the probability of no letter 'y' occupy any of their original positions?\nIf the probability can be written as the form $... | 51 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {j: 3, p: 5}, shuffle the letters in the word, what is the probability of no letter 'p' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 9 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {k: 2, v: 2, l: 2, s: 1}, shuffle the letters in the word, what is the probability of no letter 'l' occupy any of their original positions?\nIf the probability can be written as the form $... | 34 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {y: 4, w: 1, s: 1, q: 1}, shuffle the letters in the word, what is the probability of no letter 's' occupy any of their original positions?\nIf the probability can be written as the form $... | 13 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {l: 1, z: 4, j: 2, q: 2}, shuffle the letters in the word, what is the probability of no letter 'j' occupy any of their original positions?\nIf the probability can be written as the form $... | 7 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {h: 4, q: 2, l: 2}, shuffle the letters in the word, what is the probability of no letter 'q' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 12 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {p: 3, u: 3, l: 3}, shuffle the letters in the word, what is the probability of no letter 'u' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 67 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {v: 2, p: 2, q: 2, y: 1}, shuffle the letters in the word, what is the probability of no letter 'y' occupy any of their original positions?\nIf the probability can be written as the form $... | 13 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {r: 2, p: 2, f: 1, u: 1}, shuffle the letters in the word, what is the probability of no letter 'f' occupy any of their original positions?\nIf the probability can be written as the form $... | 11 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {y: 2, d: 7}, shuffle the letters in the word, what is the probability of no letter 'y' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 7 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {p: 3, l: 5}, shuffle the letters in the word, what is the probability of no letter 'p' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 43 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {b: 2, q: 1, r: 3, u: 3}, shuffle the letters in the word, what is the probability of no letter 'r' occupy any of their original positions?\nIf the probability can be written as the form $... | 67 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {a: 3, n: 3, s: 3}, shuffle the letters in the word, what is the probability of no letter 'n' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 67 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {l: 2, g: 2, m: 2}, shuffle the letters in the word, what is the probability of no letter 'l' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 23 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 6, c: 3}, shuffle the letters in the word, what is the probability of no letter 'n' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 97 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {p: 3, v: 3, t: 1, r: 2}, shuffle the letters in the word, what is the probability of no letter 'p' occupy any of their original positions?\nIf the probability can be written as the form $... | 67 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {s: 1, e: 2, g: 1, q: 2}, shuffle the letters in the word, what is the probability of no letter 'g' occupy any of their original positions?\nIf the probability can be written as the form $... | 11 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {y: 2, i: 4}, shuffle the letters in the word, what is the probability of no letter 'i' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 17 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {h: 4, v: 2, t: 3}, shuffle the letters in the word, what is the probability of no letter 'v' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 7 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {b: 7, y: 2}, shuffle the letters in the word, what is the probability of no letter 'y' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 7 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {v: 1, r: 1, n: 2, k: 2}, shuffle the letters in the word, what is the probability of no letter 'n' occupy any of their original positions?\nIf the probability can be written as the form $... | 8 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 4, r: 3}, shuffle the letters in the word, what is the probability of no letter 'n' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 44 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {b: 3, l: 2, t: 2}, shuffle the letters in the word, what is the probability of no letter 'l' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 5 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {v: 3, e: 4}, shuffle the letters in the word, what is the probability of no letter 'v' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 48 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {i: 4, y: 3}, shuffle the letters in the word, what is the probability of no letter 'i' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 44 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {d: 1, t: 5, m: 1, v: 1}, shuffle the letters in the word, what is the probability of no letter 't' occupy any of their original positions?\nIf the probability can be written as the form $... | 67 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {d: 2, e: 1, r: 2, j: 1}, shuffle the letters in the word, what is the probability of no letter 'j' occupy any of their original positions?\nIf the probability can be written as the form $... | 11 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {d: 2, y: 1, i: 3, q: 1}, shuffle the letters in the word, what is the probability of no letter 'i' occupy any of their original positions?\nIf the probability can be written as the form $... | 48 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {o: 4, a: 2}, shuffle the letters in the word, what is the probability of no letter 'a' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 23 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {e: 4, c: 3}, shuffle the letters in the word, what is the probability of no letter 'e' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 44 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {y: 3, j: 4}, shuffle the letters in the word, what is the probability of no letter 'y' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 51 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {k: 3, l: 4, t: 2}, shuffle the letters in the word, what is the probability of no letter 't' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 31 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {j: 1, v: 3, d: 2, h: 1}, shuffle the letters in the word, what is the probability of no letter 'v' occupy any of their original positions?\nIf the probability can be written as the form $... | 48 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {q: 2, x: 2, w: 3}, shuffle the letters in the word, what is the probability of no letter 'x' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 34 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {r: 1, u: 3, p: 2, d: 2}, shuffle the letters in the word, what is the probability of no letter 'u' occupy any of their original positions?\nIf the probability can be written as the form $... | 41 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {x: 3, k: 1, s: 1, a: 2}, shuffle the letters in the word, what is the probability of no letter 'x' occupy any of their original positions?\nIf the probability can be written as the form $... | 51 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {i: 2, f: 3, w: 2}, shuffle the letters in the word, what is the probability of no letter 'w' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 5 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {a: 2, s: 2, v: 1, n: 1}, shuffle the letters in the word, what is the probability of no letter 's' occupy any of their original positions?\nIf the probability can be written as the form $... | 23 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {h: 5, x: 3}, shuffle the letters in the word, what is the probability of no letter 'h' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 67 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {k: 2, r: 3, j: 2}, shuffle the letters in the word, what is the probability of no letter 'j' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 5 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {z: 1, g: 1, n: 3, y: 1}, shuffle the letters in the word, what is the probability of no letter 'z' occupy any of their original positions?\nIf the probability can be written as the form $... | 11 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {h: 3, l: 4}, shuffle the letters in the word, what is the probability of no letter 'l' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 41 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {o: 2, e: 3, l: 1, k: 2}, shuffle the letters in the word, what is the probability of no letter 'l' occupy any of their original positions?\nIf the probability can be written as the form $... | 15 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {f: 4, w: 2, d: 1}, shuffle the letters in the word, what is the probability of no letter 'f' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 44 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {z: 1, a: 2, i: 2, k: 1}, shuffle the letters in the word, what is the probability of no letter 'a' occupy any of their original positions?\nIf the probability can be written as the form $... | 23 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {r: 5, c: 1, q: 3}, shuffle the letters in the word, what is the probability of no letter 'c' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 17 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {r: 1, b: 4, k: 3}, shuffle the letters in the word, what is the probability of no letter 'r' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 15 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {b: 3, c: 3, p: 3}, shuffle the letters in the word, what is the probability of no letter 'c' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 43 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {t: 1, p: 2, d: 1, b: 3}, shuffle the letters in the word, what is the probability of no letter 'b' occupy any of their original positions?\nIf the probability can be written as the form $... | 51 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {x: 3, o: 3, f: 2}, shuffle the letters in the word, what is the probability of no letter 'o' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 43 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {j: 1, e: 3, g: 3}, shuffle the letters in the word, what is the probability of no letter 'j' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 13 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {p: 2, q: 2, f: 3, d: 1}, shuffle the letters in the word, what is the probability of no letter 'q' occupy any of their original positions?\nIf the probability can be written as the form $... | 12 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {k: 3, t: 4, z: 2}, shuffle the letters in the word, what is the probability of no letter 'z' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 7 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {q: 3, v: 4}, shuffle the letters in the word, what is the probability of no letter 'v' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 44 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {o: 3, q: 3, m: 3}, shuffle the letters in the word, what is the probability of no letter 'o' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 67 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {o: 1, g: 2, w: 2, j: 2}, shuffle the letters in the word, what is the probability of no letter 'g' occupy any of their original positions?\nIf the probability can be written as the form $... | 5 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {o: 2, v: 1, q: 3}, shuffle the letters in the word, what is the probability of no letter 'v' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 11 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {j: 1, h: 3, d: 3, u: 1}, shuffle the letters in the word, what is the probability of no letter 'h' occupy any of their original positions?\nIf the probability can be written as the form $... | 41 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {w: 3, m: 5}, shuffle the letters in the word, what is the probability of no letter 'w' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 41 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {x: 2, d: 3, o: 2}, shuffle the letters in the word, what is the probability of no letter 'o' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 34 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {g: 3, a: 1, o: 4}, shuffle the letters in the word, what is the probability of no letter 'a' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 15 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {p: 3, x: 2, e: 3}, shuffle the letters in the word, what is the probability of no letter 'x' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 47 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {s: 2, t: 4}, shuffle the letters in the word, what is the probability of no letter 's' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 23 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {b: 1, p: 2, l: 3}, shuffle the letters in the word, what is the probability of no letter 'b' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 11 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {x: 2, o: 3, y: 4}, shuffle the letters in the word, what is the probability of no letter 'o' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 67 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {j: 2, e: 2, y: 1, h: 2}, shuffle the letters in the word, what is the probability of no letter 'h' occupy any of their original positions?\nIf the probability can be written as the form $... | 34 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {b: 4, x: 4}, shuffle the letters in the word, what is the probability of no letter 'x' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 89 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {h: 3, b: 1, w: 3}, shuffle the letters in the word, what is the probability of no letter 'w' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 51 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {w: 3, z: 4}, shuffle the letters in the word, what is the probability of no letter 'z' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 44 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {m: 3, z: 3, i: 1, p: 2}, shuffle the letters in the word, what is the probability of no letter 'z' occupy any of their original positions?\nIf the probability can be written as the form $... | 67 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {l: 1, e: 2, d: 3, v: 3}, shuffle the letters in the word, what is the probability of no letter 'd' occupy any of their original positions?\nIf the probability can be written as the form $... | 67 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {m: 2, y: 4}, shuffle the letters in the word, what is the probability of no letter 'm' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 23 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 5, p: 3}, shuffle the letters in the word, what is the probability of no letter 'p' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 43 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {j: 2, q: 2, y: 2, d: 3}, shuffle the letters in the word, what is the probability of no letter 'j' occupy any of their original positions?\nIf the probability can be written as the form $... | 7 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {m: 3, b: 5}, shuffle the letters in the word, what is the probability of no letter 'm' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 41 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {g: 2, o: 2, r: 2, u: 1}, shuffle the letters in the word, what is the probability of no letter 'r' occupy any of their original positions?\nIf the probability can be written as the form $... | 5 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {q: 2, x: 3, v: 4}, shuffle the letters in the word, what is the probability of no letter 'v' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 19 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {i: 2, t: 2, r: 2}, shuffle the letters in the word, what is the probability of no letter 'r' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 8 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {c: 5, i: 1}, shuffle the letters in the word, what is the probability of no letter 'i' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 11 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {d: 1, f: 2, a: 2, q: 2}, shuffle the letters in the word, what is the probability of no letter 'q' occupy any of their original positions?\nIf the probability can be written as the form $... | 5 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {l: 3, b: 2, w: 3}, shuffle the letters in the word, what is the probability of no letter 'w' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 43 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {t: 4, e: 3, p: 2}, shuffle the letters in the word, what is the probability of no letter 'p' occupy any of their original positions?\nIf the probability can be written as the form $\\frac... | 7 | MATH |
[
{
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {p: 4, y: 3}, shuffle the letters in the word, what is the probability of no letter 'y' occupy any of their original positions?\nIf the probability can be written as the form $\\frac{m}{n}... | 48 | MATH |
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