.... Consider all permutations of the set {1, 2, n}. Prove that the average number of fixed elements in a permutation of the set -1 (n-1)dn-k (where dn is the number of 1 {1,2,...,n} is equal to k=1 (n-1)! of n elements). derangements

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A: Dear student, If you find this solution helpful please upvote ? it.

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A: H=ϕ|ϕ(n)=n=I (group of identity permutation)o(H)=1o(Sn)=n!index of H in Sn=n!1=n!

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A: Use the formula of permutation

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Q: 1. The factorial notation n! is defined for a positive number n as n! %3D п (п — 1)(п - 2)...…

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Q: that for n > k we Sn+1 ||

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Q: or disprove : [nx] =n [x] %3D for all Positive integers n > 2

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