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combinatory_probability_exactly_n_specific_fixed_train_0100
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 2, c: 3}, shuffle the letters in the word, what is the probability of exact 3 letter 'c' remains in the same position?\nIf the probability can be written as the for...
11
math
combinatory_probability_exactly_n_specific_fixed_train_0101
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {k: 2, l: 1, d: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'l' remains in the same position?\nIf the probability can be written as t...
5
math
combinatory_probability_exactly_n_specific_fixed_train_0102
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {w: 4, p: 1}, shuffle the letters in the word, what is the probability of exact 3 letter 'w' remains in the same position?\nIf the probability can be written as the for...
7
math
combinatory_probability_exactly_n_specific_fixed_train_0103
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {r: 1, c: 4}, shuffle the letters in the word, what is the probability of exact 2 letter 'c' remains in the same position?\nIf the probability can be written as the for...
6
math
combinatory_probability_exactly_n_specific_fixed_train_0104
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {g: 1, p: 1, o: 1, d: 2}, shuffle the letters in the word, what is the probability of exact 1 letter 'p' remains in the same position?\nIf the probability can be writte...
6
math
combinatory_probability_exactly_n_specific_fixed_train_0105
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {u: 4, d: 3}, shuffle the letters in the word, what is the probability of exact 2 letter 'u' remains in the same position?\nIf the probability can be written as the for...
9
math
combinatory_probability_exactly_n_specific_fixed_train_0106
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {c: 1, e: 3}, shuffle the letters in the word, what is the probability of exact 3 letter 'e' remains in the same position?\nIf the probability can be written as the for...
5
math
combinatory_probability_exactly_n_specific_fixed_train_0107
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {d: 1, h: 1, n: 1, i: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'd' remains in the same position?\nIf the probability can be writte...
5
math
combinatory_probability_exactly_n_specific_fixed_train_0108
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {s: 3, e: 2, w: 2}, shuffle the letters in the word, what is the probability of exact 2 letter 'w' remains in the same position?\nIf the probability can be written as t...
22
math
combinatory_probability_exactly_n_specific_fixed_train_0109
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {l: 2, g: 1, c: 3, z: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'z' remains in the same position?\nIf the probability can be writte...
8
math
combinatory_probability_exactly_n_specific_fixed_train_0110
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {a: 1, z: 2, k: 1, s: 3}, shuffle the letters in the word, what is the probability of exact 3 letter 's' remains in the same position?\nIf the probability can be writte...
36
math
combinatory_probability_exactly_n_specific_fixed_train_0111
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {v: 1, s: 1, x: 2, j: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'j' remains in the same position?\nIf the probability can be writte...
6
math
combinatory_probability_exactly_n_specific_fixed_train_0112
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {u: 1, f: 1, c: 1, x: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'f' remains in the same position?\nIf the probability can be writte...
5
math
combinatory_probability_exactly_n_specific_fixed_train_0113
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {p: 2, i: 1, u: 3, z: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'z' remains in the same position?\nIf the probability can be writte...
8
math
combinatory_probability_exactly_n_specific_fixed_train_0114
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {w: 1, d: 1, q: 1, c: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'd' remains in the same position?\nIf the probability can be writte...
5
math
combinatory_probability_exactly_n_specific_fixed_train_0115
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {j: 4, v: 3}, shuffle the letters in the word, what is the probability of exact 2 letter 'v' remains in the same position?\nIf the probability can be written as the for...
8
math
combinatory_probability_exactly_n_specific_fixed_train_0116
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {f: 2, y: 4}, shuffle the letters in the word, what is the probability of exact 1 letter 'f' remains in the same position?\nIf the probability can be written as the for...
4
math
combinatory_probability_exactly_n_specific_fixed_train_0117
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {e: 4, m: 2}, shuffle the letters in the word, what is the probability of exact 2 letter 'e' remains in the same position?\nIf the probability can be written as the for...
7
math
combinatory_probability_exactly_n_specific_fixed_train_0118
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {y: 3, k: 2}, shuffle the letters in the word, what is the probability of exact 2 letter 'y' remains in the same position?\nIf the probability can be written as the for...
13
math
combinatory_probability_exactly_n_specific_fixed_train_0119
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {w: 1, z: 2, i: 2}, shuffle the letters in the word, what is the probability of exact 2 letter 'i' remains in the same position?\nIf the probability can be written as t...
11
math
combinatory_probability_exactly_n_specific_fixed_train_0120
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {r: 1, k: 2, g: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'k' remains in the same position?\nIf the probability can be written as t...
3
math
combinatory_probability_exactly_n_specific_fixed_train_0121
combinatory_probability_exactly_n_specific_fixed
null
[ { "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: 3, t: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'e' remains in the same position?\nIf the probability can be written as t...
3
math
combinatory_probability_exactly_n_specific_fixed_train_0122
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {d: 3, y: 3, o: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'o' remains in the same position?\nIf the probability can be written as t...
8
math
combinatory_probability_exactly_n_specific_fixed_train_0123
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {y: 5, j: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'j' remains in the same position?\nIf the probability can be written as the for...
7
math
combinatory_probability_exactly_n_specific_fixed_train_0124
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {b: 3, f: 2, t: 1, v: 1}, shuffle the letters in the word, what is the probability of exact 2 letter 'f' remains in the same position?\nIf the probability can be writte...
22
math
combinatory_probability_exactly_n_specific_fixed_train_0125
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 3, q: 3}, shuffle the letters in the word, what is the probability of exact 2 letter 'n' remains in the same position?\nIf the probability can be written as the for...
23
math
combinatory_probability_exactly_n_specific_fixed_train_0126
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {v: 1, k: 3, e: 2, i: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'e' remains in the same position?\nIf the probability can be writte...
9
math
combinatory_probability_exactly_n_specific_fixed_train_0127
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {l: 1, d: 1, m: 1, z: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'm' remains in the same position?\nIf the probability can be writte...
5
math
combinatory_probability_exactly_n_specific_fixed_train_0128
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 1, z: 1, e: 4}, shuffle the letters in the word, what is the probability of exact 1 letter 'z' remains in the same position?\nIf the probability can be written as t...
7
math
combinatory_probability_exactly_n_specific_fixed_train_0129
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {e: 1, q: 2, p: 3, g: 1}, shuffle the letters in the word, what is the probability of exact 2 letter 'q' remains in the same position?\nIf the probability can be writte...
22
math
combinatory_probability_exactly_n_specific_fixed_train_0130
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {i: 3, s: 1}, shuffle the letters in the word, what is the probability of exact 2 letter 'i' remains in the same position?\nIf the probability can be written as the for...
3
math
combinatory_probability_exactly_n_specific_fixed_train_0131
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {x: 1, z: 1, h: 1, v: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'x' remains in the same position?\nIf the probability can be writte...
5
math
combinatory_probability_exactly_n_specific_fixed_train_0132
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {z: 3, y: 1, m: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'z' remains in the same position?\nIf the probability can be written as t...
3
math
combinatory_probability_exactly_n_specific_fixed_train_0133
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {b: 3, c: 1, l: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'b' remains in the same position?\nIf the probability can be written as t...
3
math
combinatory_probability_exactly_n_specific_fixed_train_0134
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {t: 2, q: 1, e: 3}, shuffle the letters in the word, what is the probability of exact 1 letter 'q' remains in the same position?\nIf the probability can be written as t...
7
math
combinatory_probability_exactly_n_specific_fixed_train_0135
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {v: 3, d: 4}, shuffle the letters in the word, what is the probability of exact 3 letter 'd' remains in the same position?\nIf the probability can be written as the for...
39
math
combinatory_probability_exactly_n_specific_fixed_train_0136
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {a: 2, z: 2, h: 2, p: 1}, shuffle the letters in the word, what is the probability of exact 2 letter 'z' remains in the same position?\nIf the probability can be writte...
22
math
combinatory_probability_exactly_n_specific_fixed_train_0137
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {w: 3, g: 2, e: 2}, shuffle the letters in the word, what is the probability of exact 1 letter 'e' remains in the same position?\nIf the probability can be written as t...
9
math
combinatory_probability_exactly_n_specific_fixed_train_0138
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {p: 1, g: 3, h: 1}, shuffle the letters in the word, what is the probability of exact 2 letter 'g' remains in the same position?\nIf the probability can be written as t...
13
math
combinatory_probability_exactly_n_specific_fixed_train_0139
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {b: 1, h: 1, f: 2}, shuffle the letters in the word, what is the probability of exact 1 letter 'h' remains in the same position?\nIf the probability can be written as t...
5
math
combinatory_probability_exactly_n_specific_fixed_train_0140
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {r: 1, o: 1, l: 1, j: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'o' remains in the same position?\nIf the probability can be writte...
5
math
combinatory_probability_exactly_n_specific_fixed_train_0141
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {j: 2, c: 1, i: 1, s: 1}, shuffle the letters in the word, what is the probability of exact 2 letter 'j' remains in the same position?\nIf the probability can be writte...
11
math
combinatory_probability_exactly_n_specific_fixed_train_0142
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {p: 1, n: 2, l: 2, z: 2}, shuffle the letters in the word, what is the probability of exact 1 letter 'z' remains in the same position?\nIf the probability can be writte...
26
math
combinatory_probability_exactly_n_specific_fixed_train_0143
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {b: 1, c: 1, s: 1, p: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'b' remains in the same position?\nIf the probability can be writte...
5
math
combinatory_probability_exactly_n_specific_fixed_train_0144
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {d: 4, o: 2}, shuffle the letters in the word, what is the probability of exact 1 letter 'd' remains in the same position?\nIf the probability can be written as the for...
19
math
combinatory_probability_exactly_n_specific_fixed_train_0145
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {y: 3, t: 4}, shuffle the letters in the word, what is the probability of exact 3 letter 't' remains in the same position?\nIf the probability can be written as the for...
39
math
combinatory_probability_exactly_n_specific_fixed_train_0146
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {s: 3, w: 1, d: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'w' remains in the same position?\nIf the probability can be written as t...
6
math
combinatory_probability_exactly_n_specific_fixed_train_0147
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {g: 1, q: 2, l: 2}, shuffle the letters in the word, what is the probability of exact 2 letter 'l' remains in the same position?\nIf the probability can be written as t...
11
math
combinatory_probability_exactly_n_specific_fixed_train_0148
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {j: 2, h: 1, f: 3}, shuffle the letters in the word, what is the probability of exact 1 letter 'j' remains in the same position?\nIf the probability can be written as t...
19
math
combinatory_probability_exactly_n_specific_fixed_train_0149
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {n: 1, s: 2, c: 1, i: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'n' remains in the same position?\nIf the probability can be writte...
6
math
combinatory_probability_exactly_n_specific_fixed_train_0150
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {w: 2, d: 3, e: 2}, shuffle the letters in the word, what is the probability of exact 1 letter 'e' remains in the same position?\nIf the probability can be written as t...
9
math
combinatory_probability_exactly_n_specific_fixed_train_0151
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {i: 4, p: 3}, shuffle the letters in the word, what is the probability of exact 2 letter 'p' remains in the same position?\nIf the probability can be written as the for...
8
math
combinatory_probability_exactly_n_specific_fixed_train_0152
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {y: 2, c: 2, d: 2, i: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'd' remains in the same position?\nIf the probability can be writte...
9
math
combinatory_probability_exactly_n_specific_fixed_train_0153
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {m: 4, g: 1, w: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'w' remains in the same position?\nIf the probability can be written as t...
7
math
combinatory_probability_exactly_n_specific_fixed_train_0154
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {e: 4, l: 3}, shuffle the letters in the word, what is the probability of exact 2 letter 'e' remains in the same position?\nIf the probability can be written as the for...
9
math
combinatory_probability_exactly_n_specific_fixed_train_0155
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {j: 1, i: 1, t: 2}, shuffle the letters in the word, what is the probability of exact 1 letter 'j' remains in the same position?\nIf the probability can be written as t...
5
math
combinatory_probability_exactly_n_specific_fixed_train_0156
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {w: 1, j: 3, q: 1}, shuffle the letters in the word, what is the probability of exact 3 letter 'j' remains in the same position?\nIf the probability can be written as t...
11
math
combinatory_probability_exactly_n_specific_fixed_train_0157
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {m: 2, n: 1, a: 2, p: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'p' remains in the same position?\nIf the probability can be writte...
7
math
combinatory_probability_exactly_n_specific_fixed_train_0158
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {j: 1, r: 1, l: 1, i: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'r' remains in the same position?\nIf the probability can be writte...
5
math
combinatory_probability_exactly_n_specific_fixed_train_0159
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {m: 2, y: 1, i: 1, v: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'v' remains in the same position?\nIf the probability can be writte...
6
math
combinatory_probability_exactly_n_specific_fixed_train_0160
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {w: 2, v: 2}, shuffle the letters in the word, what is the probability of exact 2 letter 'w' remains in the same position?\nIf the probability can be written as the for...
7
math
combinatory_probability_exactly_n_specific_fixed_train_0161
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {c: 5, w: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'c' remains in the same position?\nIf the probability can be written as the for...
4
math
combinatory_probability_exactly_n_specific_fixed_train_0162
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {l: 1, c: 2, q: 2, h: 2}, shuffle the letters in the word, what is the probability of exact 2 letter 'q' remains in the same position?\nIf the probability can be writte...
22
math
combinatory_probability_exactly_n_specific_fixed_train_0163
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {d: 2, j: 1, w: 2}, shuffle the letters in the word, what is the probability of exact 1 letter 'j' remains in the same position?\nIf the probability can be written as t...
6
math
combinatory_probability_exactly_n_specific_fixed_train_0164
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {h: 4, o: 2}, shuffle the letters in the word, what is the probability of exact 1 letter 'h' remains in the same position?\nIf the probability can be written as the for...
22
math
combinatory_probability_exactly_n_specific_fixed_train_0165
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {k: 1, z: 1, o: 1, u: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'o' remains in the same position?\nIf the probability can be writte...
5
math
combinatory_probability_exactly_n_specific_fixed_train_0166
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {d: 3, y: 2, h: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'h' remains in the same position?\nIf the probability can be written as t...
7
math
combinatory_probability_exactly_n_specific_fixed_train_0167
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {r: 2, c: 2, d: 1, i: 2}, shuffle the letters in the word, what is the probability of exact 2 letter 'i' remains in the same position?\nIf the probability can be writte...
22
math
combinatory_probability_exactly_n_specific_fixed_train_0168
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {x: 1, u: 1, g: 1, s: 2}, shuffle the letters in the word, what is the probability of exact 1 letter 's' remains in the same position?\nIf the probability can be writte...
7
math
combinatory_probability_exactly_n_specific_fixed_train_0169
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {c: 1, z: 1, w: 2, e: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'w' remains in the same position?\nIf the probability can be writte...
7
math
combinatory_probability_exactly_n_specific_fixed_train_0170
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 2, j: 1, h: 1, e: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'j' remains in the same position?\nIf the probability can be writte...
6
math
combinatory_probability_exactly_n_specific_fixed_train_0171
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {r: 2, z: 3, y: 2}, shuffle the letters in the word, what is the probability of exact 1 letter 'r' remains in the same position?\nIf the probability can be written as t...
9
math
combinatory_probability_exactly_n_specific_fixed_train_0172
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {n: 1, e: 1, s: 1, o: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'o' remains in the same position?\nIf the probability can be writte...
5
math
combinatory_probability_exactly_n_specific_fixed_train_0173
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {g: 1, i: 1, a: 1, d: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'a' remains in the same position?\nIf the probability can be writte...
5
math
combinatory_probability_exactly_n_specific_fixed_train_0174
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {m: 2, c: 3, e: 2}, shuffle the letters in the word, what is the probability of exact 1 letter 'c' remains in the same position?\nIf the probability can be written as t...
9
math
combinatory_probability_exactly_n_specific_fixed_train_0175
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {r: 1, z: 5}, shuffle the letters in the word, what is the probability of exact 2 letter 'z' remains in the same position?\nIf the probability can be written as the for...
5
math
combinatory_probability_exactly_n_specific_fixed_train_0176
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {l: 3, r: 2, j: 2}, shuffle the letters in the word, what is the probability of exact 2 letter 'l' remains in the same position?\nIf the probability can be written as t...
8
math
combinatory_probability_exactly_n_specific_fixed_train_0177
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {k: 1, u: 1, j: 1, v: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'v' remains in the same position?\nIf the probability can be writte...
5
math
combinatory_probability_exactly_n_specific_fixed_train_0178
combinatory_probability_exactly_n_specific_fixed
null
[ { "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: 1, r: 2}, shuffle the letters in the word, what is the probability of exact 1 letter 'r' remains in the same position?\nIf the probability can be written as t...
4
math
combinatory_probability_exactly_n_specific_fixed_train_0179
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {w: 2, d: 1, a: 1, v: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'w' remains in the same position?\nIf the probability can be writte...
7
math
combinatory_probability_exactly_n_specific_fixed_train_0180
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {b: 2, p: 5}, shuffle the letters in the word, what is the probability of exact 1 letter 'b' remains in the same position?\nIf the probability can be written as the for...
9
math
combinatory_probability_exactly_n_specific_fixed_train_0181
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {o: 1, b: 2, x: 1, n: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'x' remains in the same position?\nIf the probability can be writte...
6
math
combinatory_probability_exactly_n_specific_fixed_train_0182
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {i: 1, m: 1, x: 1, d: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'm' remains in the same position?\nIf the probability can be writte...
5
math
combinatory_probability_exactly_n_specific_fixed_train_0183
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {b: 3, f: 1, p: 2}, shuffle the letters in the word, what is the probability of exact 1 letter 'b' remains in the same position?\nIf the probability can be written as t...
29
math
combinatory_probability_exactly_n_specific_fixed_train_0184
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {g: 2, f: 2}, shuffle the letters in the word, what is the probability of exact 2 letter 'g' remains in the same position?\nIf the probability can be written as the for...
7
math
combinatory_probability_exactly_n_specific_fixed_train_0185
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {c: 2, j: 1, p: 1}, shuffle the letters in the word, what is the probability of exact 2 letter 'c' remains in the same position?\nIf the probability can be written as t...
7
math
combinatory_probability_exactly_n_specific_fixed_train_0186
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {u: 4, m: 1, o: 2}, shuffle the letters in the word, what is the probability of exact 1 letter 'm' remains in the same position?\nIf the probability can be written as t...
8
math
combinatory_probability_exactly_n_specific_fixed_train_0187
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {a: 2, n: 4}, shuffle the letters in the word, what is the probability of exact 1 letter 'n' remains in the same position?\nIf the probability can be written as the for...
22
math
combinatory_probability_exactly_n_specific_fixed_train_0188
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {x: 3, o: 1, d: 3}, shuffle the letters in the word, what is the probability of exact 2 letter 'd' remains in the same position?\nIf the probability can be written as t...
39
math
combinatory_probability_exactly_n_specific_fixed_train_0189
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {g: 1, l: 2, m: 2}, shuffle the letters in the word, what is the probability of exact 1 letter 'm' remains in the same position?\nIf the probability can be written as t...
7
math
combinatory_probability_exactly_n_specific_fixed_train_0190
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {q: 1, w: 1, t: 1, g: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'w' remains in the same position?\nIf the probability can be writte...
5
math
combinatory_probability_exactly_n_specific_fixed_train_0191
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {y: 1, q: 2, h: 1, f: 2}, shuffle the letters in the word, what is the probability of exact 1 letter 'f' remains in the same position?\nIf the probability can be writte...
19
math
combinatory_probability_exactly_n_specific_fixed_train_0192
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {i: 1, v: 2, t: 2, f: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'i' remains in the same position?\nIf the probability can be writte...
7
math
combinatory_probability_exactly_n_specific_fixed_train_0193
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {q: 1, g: 1, r: 1, a: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'g' remains in the same position?\nIf the probability can be writte...
5
math
combinatory_probability_exactly_n_specific_fixed_train_0194
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {s: 1, o: 2, f: 2, r: 2}, shuffle the letters in the word, what is the probability of exact 2 letter 'o' remains in the same position?\nIf the probability can be writte...
22
math
combinatory_probability_exactly_n_specific_fixed_train_0195
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {j: 2, b: 3}, shuffle the letters in the word, what is the probability of exact 1 letter 'j' remains in the same position?\nIf the probability can be written as the for...
13
math
combinatory_probability_exactly_n_specific_fixed_train_0196
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {o: 1, h: 1, u: 2, k: 1}, shuffle the letters in the word, what is the probability of exact 1 letter 'o' remains in the same position?\nIf the probability can be writte...
6
math
combinatory_probability_exactly_n_specific_fixed_train_0197
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {j: 5, r: 1, f: 1}, shuffle the letters in the word, what is the probability of exact 2 letter 'j' remains in the same position?\nIf the probability can be written as t...
31
math
combinatory_probability_exactly_n_specific_fixed_train_0198
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 3 letters from the multiset {s: 4, m: 3}, shuffle the letters in the word, what is the probability of exact 3 letter 'm' remains in the same position?\nIf the probability can be written as the for...
36
math
combinatory_probability_exactly_n_specific_fixed_train_0199
combinatory_probability_exactly_n_specific_fixed
null
[ { "role": "user", "content": "What is the probability of such event happening: Form a word by randomly choosing 2 letters from the multiset {o: 3, b: 2}, shuffle the letters in the word, what is the probability of exact 2 letter 'b' remains in the same position?\nIf the probability can be written as the for...
11
math