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math_combinatory_probability_no_fixed_points_level_4

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train · 1k rows

messages listlengths 1 1	ground_truth stringclasses 7 values	dataset stringclasses 1 value
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {i: 1, r: 3, e: 3, v: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	659	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {t: 3, x: 3, j: 3, i: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	659	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {k: 3, r: 2, u: 3, s: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	1501	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {f: 2, d: 2, h: 2, g: 4}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	33	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {w: 2, v: 2, d: 3, e: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	1501	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {d: 3, o: 3, n: 1, c: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	659	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {n: 3, e: 2, b: 3, u: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	1501	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {u: 4, p: 1, n: 3, x: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	367	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {f: 2, q: 3, t: 3, l: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	1501	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {f: 4, y: 1, w: 4, z: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	8	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {m: 2, r: 1, g: 2, u: 5}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	8	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {b: 2, p: 4, c: 1, f: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	367	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {f: 3, z: 2, w: 3, s: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	1501	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {i: 1, z: 1, v: 2, o: 6}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	139	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {b: 3, d: 3, y: 2, g: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	1501	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {m: 2, c: 1, e: 2, t: 5}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	8	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {r: 2, d: 3, k: 2, c: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	1501	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {z: 2, n: 3, e: 2, o: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	1501	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {w: 1, e: 2, v: 2, a: 5}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	8	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {x: 2, u: 2, j: 2, t: 4}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	33	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {q: 3, i: 3, y: 3, z: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	659	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {t: 3, l: 2, o: 3, h: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	1501	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {f: 2, e: 2, r: 3, y: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	1501	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {g: 3, n: 2, q: 2, c: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	1501	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {h: 2, j: 3, y: 2, t: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	1501	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {r: 3, x: 1, k: 4, b: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	367	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {g: 3, f: 4, d: 1, o: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	367	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {w: 5, k: 2, c: 1, e: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	8	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {p: 1, g: 3, k: 2, n: 4}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	367	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {d: 2, g: 2, n: 4, j: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	33	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {s: 2, b: 3, i: 2, e: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	1501	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {u: 3, q: 1, m: 3, o: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	659	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {z: 1, k: 5, y: 1, l: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	5707	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {j: 2, p: 3, k: 4, b: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	367	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {n: 2, a: 1, w: 5, e: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	8	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {q: 4, x: 2, r: 2, m: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	33	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {y: 1, n: 1, i: 4, z: 4}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	8	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {i: 1, o: 4, v: 3, f: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	367	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {g: 1, w: 2, k: 1, s: 6}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	139	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {v: 5, y: 3, x: 1, b: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	5707	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {y: 2, t: 3, i: 2, r: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	1501	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {w: 5, t: 3, z: 1, m: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	5707	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {k: 2, z: 2, e: 3, t: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	1501	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {w: 1, j: 2, c: 3, z: 4}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	367	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {v: 2, o: 3, q: 2, m: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	1501	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {y: 1, d: 2, w: 5, i: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	8	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {p: 3, l: 2, d: 3, e: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	1501	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {w: 2, x: 2, h: 3, f: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	1501	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {v: 2, c: 2, s: 4, t: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	33	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {j: 3, h: 3, w: 2, q: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	1501	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {w: 2, v: 1, a: 5, k: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	8	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {b: 2, p: 3, s: 1, k: 4}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	367	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {g: 1, s: 4, y: 2, c: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	367	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {w: 1, g: 4, n: 1, v: 4}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	8	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {p: 2, a: 3, r: 2, o: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	1501	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {j: 2, w: 2, r: 3, p: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	1501	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {v: 2, r: 2, i: 2, u: 4}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	33	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {u: 2, h: 1, x: 3, j: 4}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	367	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {o: 3, p: 2, z: 2, h: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	1501	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {l: 2, q: 4, j: 3, z: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	367	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {k: 1, p: 6, d: 1, h: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	139	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {r: 1, x: 2, j: 4, u: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	367	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {j: 5, o: 2, f: 2, a: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	8	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {r: 4, i: 2, m: 2, v: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	33	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {j: 1, t: 3, h: 3, g: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	659	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {o: 1, r: 3, y: 3, q: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	659	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {g: 3, f: 4, d: 2, y: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	367	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {m: 3, t: 2, b: 3, h: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	1501	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {g: 4, q: 2, d: 2, b: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	33	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {e: 2, n: 3, m: 2, s: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	1501	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {q: 5, z: 1, c: 2, g: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	8	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {c: 2, d: 3, f: 4, x: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	367	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {x: 1, l: 3, r: 3, q: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	659	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {h: 2, r: 1, i: 4, y: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	367	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {n: 1, t: 3, s: 3, i: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	659	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {i: 2, k: 2, s: 4, p: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	33	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {i: 2, w: 5, o: 1, a: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	8	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {b: 1, h: 3, e: 3, w: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	659	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {o: 2, k: 2, m: 1, p: 5}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	8	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {h: 2, z: 3, j: 1, p: 4}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	367	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {q: 2, r: 1, n: 4, v: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	367	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {i: 4, q: 2, l: 2, h: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	33	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {y: 2, s: 2, g: 2, e: 4}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	33	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {w: 1, g: 2, i: 2, f: 5}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	8	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {c: 2, d: 3, a: 2, m: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	1501	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {f: 3, d: 2, x: 3, g: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	1501	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {b: 2, k: 3, s: 3, f: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	1501	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {x: 2, m: 1, n: 6, w: 1}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	139	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {e: 2, c: 1, j: 3, u: 4}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	367	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {p: 1, s: 4, u: 3, b: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	367	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {b: 2, c: 3, r: 1, o: 4}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	367	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {l: 3, y: 4, t: 1, h: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	367	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {o: 3, p: 2, z: 1, x: 4}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	367	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {o: 3, y: 2, v: 1, m: 4}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	367	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {a: 2, q: 1, f: 2, v: 5}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	8	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {s: 4, l: 1, h: 2, z: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	367	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {u: 1, g: 2, n: 5, b: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	8	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {z: 4, t: 1, x: 3, h: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	367	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {o: 3, f: 2, i: 2, u: 3}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	1501	MATH
[ { "content": "What is the probability of such event happening: Form a word by randomly choosing 4 letters from the multiset {g: 3, f: 3, d: 2, t: 2}, shuffle the letters in the word, what is the probability of no same letter remains in its original position?\nIf the probability can be written as the form $\\fra...	1501	MATH

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