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π Of N Numbers. Let C Denote The Total Number Of Cycles In π. (a) (5 Pt) Find P(C = 1), The Probability That A Random Permutation Consists Of A Single Cycle. Answer: P(C = 1) = # Possible Cycles Of Length N N! = (n−1)! N! = 1 N. (b) (8 Pt) Find The Expected Number E[C] Of Cycles For N = 2 And N = 3. Answer: Let (i 1i 2...i K) Denote A Cycle ... 3th, 2024

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