id stringlengths 39 39 | setting_key stringclasses 1
value | setting_name stringclasses 1
value | messages listlengths 1 1 | ground_truth stringclasses 167
values | dataset stringclasses 1
value |
|---|---|---|---|---|---|
comp_parametric_intersection_train_0600 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {t: 3, i: 2, h: 2}, 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... | 5 | math |
comp_parametric_intersection_train_0601 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {w: 2, l: 1, m: 2, j: 1}, 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 w... | 8 | math |
comp_parametric_intersection_train_0602 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {x: 1, m: 2, d: 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 w... | 23 | math |
comp_parametric_intersection_train_0603 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {z: 3, a: 1, 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... | 23 | math |
comp_parametric_intersection_train_0604 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {e: 3, o: 5}, 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 th... | 41 | math |
comp_parametric_intersection_train_0605 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {s: 3, t: 3}, 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 th... | 5 | math |
comp_parametric_intersection_train_0606 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {b: 2, e: 2, f: 2, h: 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 w... | 47 | math |
comp_parametric_intersection_train_0607 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {s: 2, e: 2, f: 1, y: 1}, 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 w... | 23 | math |
comp_parametric_intersection_train_0608 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {o: 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 th... | 44 | math |
comp_parametric_intersection_train_0609 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {j: 2, m: 3, x: 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... | 47 | math |
comp_parametric_intersection_train_0610 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {x: 2, b: 1, t: 2, r: 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 w... | 15 | math |
comp_parametric_intersection_train_0611 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {g: 6, m: 2}, 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 th... | 12 | math |
comp_parametric_intersection_train_0612 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {p: 4, i: 2}, 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 th... | 8 | math |
comp_parametric_intersection_train_0613 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {k: 3, j: 4}, 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 th... | 41 | math |
comp_parametric_intersection_train_0614 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {q: 1, d: 1, s: 2, u: 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 w... | 48 | math |
comp_parametric_intersection_train_0615 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {t: 5, c: 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 th... | 34 | math |
comp_parametric_intersection_train_0616 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {k: 4, x: 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 th... | 48 | math |
comp_parametric_intersection_train_0617 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {z: 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 th... | 67 | math |
comp_parametric_intersection_train_0618 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {w: 2, k: 1, l: 2, t: 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 w... | 13 | math |
comp_parametric_intersection_train_0619 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {o: 2, u: 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 th... | 8 | math |
comp_parametric_intersection_train_0620 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {a: 3, s: 3}, 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 th... | 27 | math |
comp_parametric_intersection_train_0621 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {m: 2, q: 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... | 34 | math |
comp_parametric_intersection_train_0622 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {g: 2, 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 th... | 16 | math |
comp_parametric_intersection_train_0623 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {q: 1, a: 2, k: 1, n: 3}, 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 w... | 34 | math |
comp_parametric_intersection_train_0624 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {y: 1, q: 2, s: 5}, 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... | 67 | math |
comp_parametric_intersection_train_0625 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {m: 2, w: 1, e: 1, q: 2}, 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 w... | 23 | math |
comp_parametric_intersection_train_0626 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {h: 1, x: 1, n: 3, r: 1}, 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 w... | 11 | math |
comp_parametric_intersection_train_0627 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {x: 2, z: 3, b: 1, t: 2}, 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 w... | 15 | math |
comp_parametric_intersection_train_0628 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {s: 1, v: 1, f: 2, 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 w... | 8 | math |
comp_parametric_intersection_train_0629 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {g: 2, n: 1, p: 2, z: 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 w... | 34 | math |
comp_parametric_intersection_train_0630 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {y: 4, e: 4}, 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 th... | 19 | math |
comp_parametric_intersection_train_0631 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {e: 3, n: 5}, 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 th... | 9 | math |
comp_parametric_intersection_train_0632 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {m: 5, c: 2}, 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 th... | 23 | math |
comp_parametric_intersection_train_0633 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {n: 3, v: 2, c: 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... | 34 | math |
comp_parametric_intersection_train_0634 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {o: 2, e: 1, y: 2, a: 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 w... | 5 | math |
comp_parametric_intersection_train_0635 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {v: 2, c: 1, q: 1, n: 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 w... | 34 | math |
comp_parametric_intersection_train_0636 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {z: 3, x: 3, m: 2}, 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... | 12 | math |
comp_parametric_intersection_train_0637 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {r: 3, i: 3, q: 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... | 43 | math |
comp_parametric_intersection_train_0638 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {o: 2, s: 1, l: 2, w: 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 w... | 8 | math |
comp_parametric_intersection_train_0639 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {c: 3, u: 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 th... | 27 | math |
comp_parametric_intersection_train_0640 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {s: 2, w: 1, l: 1, n: 3}, 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 w... | 34 | math |
comp_parametric_intersection_train_0641 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {t: 1, s: 3, r: 2, b: 1}, 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 w... | 13 | math |
comp_parametric_intersection_train_0642 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {l: 2, k: 5}, 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 th... | 22 | math |
comp_parametric_intersection_train_0643 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {b: 5, n: 2}, 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 th... | 23 | math |
comp_parametric_intersection_train_0644 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {w: 3, k: 1, j: 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... | 11 | math |
comp_parametric_intersection_train_0645 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {e: 4, l: 2, q: 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... | 13 | math |
comp_parametric_intersection_train_0646 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {z: 1, e: 1, s: 5, o: 1}, 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 w... | 15 | math |
comp_parametric_intersection_train_0647 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {w: 1, c: 2, o: 1, s: 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 w... | 8 | math |
comp_parametric_intersection_train_0648 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {i: 5, 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 th... | 5 | math |
comp_parametric_intersection_train_0649 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {a: 5, m: 2}, 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 th... | 34 | math |
comp_parametric_intersection_train_0650 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {f: 3, g: 2, k: 2, z: 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 w... | 41 | math |
comp_parametric_intersection_train_0651 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {j: 1, b: 3, e: 2}, 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... | 5 | math |
comp_parametric_intersection_train_0652 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {j: 4, v: 3, p: 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... | 89 | math |
comp_parametric_intersection_train_0653 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {z: 2, n: 3, g: 3}, 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... | 43 | math |
comp_parametric_intersection_train_0654 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {l: 4, p: 4}, 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 th... | 89 | math |
comp_parametric_intersection_train_0655 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {q: 4, c: 3}, 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 th... | 41 | math |
comp_parametric_intersection_train_0656 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {r: 1, o: 1, w: 2, m: 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 w... | 23 | math |
comp_parametric_intersection_train_0657 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {z: 2, o: 6}, 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 th... | 12 | math |
comp_parametric_intersection_train_0658 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {g: 1, m: 2, d: 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... | 27 | math |
comp_parametric_intersection_train_0659 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {y: 4, h: 4}, 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 th... | 89 | math |
comp_parametric_intersection_train_0660 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {f: 3, e: 5}, 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 th... | 41 | math |
comp_parametric_intersection_train_0661 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {h: 1, z: 2, e: 2, 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 w... | 5 | math |
comp_parametric_intersection_train_0662 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {x: 4, k: 3, y: 1}, 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... | 41 | math |
comp_parametric_intersection_train_0663 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {e: 2, m: 1, j: 1, s: 2}, 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 w... | 8 | math |
comp_parametric_intersection_train_0664 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {f: 4, 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 th... | 23 | math |
comp_parametric_intersection_train_0665 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {l: 3, t: 4}, 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 th... | 41 | math |
comp_parametric_intersection_train_0666 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {e: 4, x: 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 th... | 48 | math |
comp_parametric_intersection_train_0667 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {o: 1, u: 1, t: 2, z: 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 w... | 11 | math |
comp_parametric_intersection_train_0668 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {q: 3, g: 5}, 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 th... | 43 | math |
comp_parametric_intersection_train_0669 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {v: 2, n: 1, z: 1, o: 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 w... | 8 | math |
comp_parametric_intersection_train_0670 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {m: 3, v: 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 th... | 48 | math |
comp_parametric_intersection_train_0671 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {n: 3, z: 5}, 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 th... | 9 | math |
comp_parametric_intersection_train_0672 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {y: 3, r: 2, g: 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... | 34 | math |
comp_parametric_intersection_train_0673 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {e: 2, i: 1, g: 1, b: 2}, 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 w... | 8 | math |
comp_parametric_intersection_train_0674 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {v: 2, w: 2, y: 2, o: 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 w... | 12 | math |
comp_parametric_intersection_train_0675 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 2, g: 4}, 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 th... | 17 | math |
comp_parametric_intersection_train_0676 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {f: 4, y: 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 th... | 89 | math |
comp_parametric_intersection_train_0677 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {o: 3, i: 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 th... | 51 | math |
comp_parametric_intersection_train_0678 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {g: 5, k: 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 th... | 22 | math |
comp_parametric_intersection_train_0679 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {l: 2, j: 1, e: 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... | 34 | math |
comp_parametric_intersection_train_0680 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {x: 1, v: 2, a: 3}, 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... | 5 | math |
comp_parametric_intersection_train_0681 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {s: 2, h: 2, k: 2, x: 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 w... | 12 | math |
comp_parametric_intersection_train_0682 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {b: 3, x: 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 th... | 27 | math |
comp_parametric_intersection_train_0683 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {w: 2, m: 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... | 89 | math |
comp_parametric_intersection_train_0684 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {t: 4, 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 th... | 8 | math |
comp_parametric_intersection_train_0685 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {t: 6, k: 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 th... | 15 | math |
comp_parametric_intersection_train_0686 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {y: 2, o: 1, a: 3, i: 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 w... | 34 | math |
comp_parametric_intersection_train_0687 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {d: 2, r: 1, b: 2, a: 2}, 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 w... | 5 | math |
comp_parametric_intersection_train_0688 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {h: 5, j: 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 th... | 67 | math |
comp_parametric_intersection_train_0689 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {h: 1, z: 4, x: 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... | 13 | math |
comp_parametric_intersection_train_0690 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {n: 1, c: 4, t: 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... | 13 | math |
comp_parametric_intersection_train_0691 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {h: 2, q: 1, g: 4}, 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... | 34 | math |
comp_parametric_intersection_train_0692 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {y: 1, g: 1, d: 2, o: 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 w... | 11 | math |
comp_parametric_intersection_train_0693 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {v: 2, c: 3, h: 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... | 43 | math |
comp_parametric_intersection_train_0694 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {n: 2, h: 2, l: 1, u: 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 w... | 13 | math |
comp_parametric_intersection_train_0695 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {a: 1, l: 2, o: 3, q: 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 w... | 5 | math |
comp_parametric_intersection_train_0696 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {t: 2, w: 1, a: 3}, 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... | 27 | math |
comp_parametric_intersection_train_0697 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {j: 4, i: 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 th... | 41 | math |
comp_parametric_intersection_train_0698 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {l: 4, r: 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 th... | 48 | math |
comp_parametric_intersection_train_0699 | comp_parametric_intersection | Combinatorics (Probability) + Algebra (Function Intersection) | [
{
"role": "user",
"content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {b: 1, l: 1, q: 3, z: 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 w... | 13 | math |
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