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(1) How many permutations S7 are such that 4 = id? (2) How many permutations Sn contain 1,2, and 3 in the same cycle? (3)

(1) How many permutations S7 are such that 4 = id? (2) How many permutations Sn contain 1,2, and 3 in the same cycle? (3) We select a permutation in Sn at random. What is the probability that n is in a cycle of length k.

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