ISI 2017

[Prakash Kapadia]

Let A = {1,2,...,n}. For a permutation P = ( P(1),P(2),...,P(n) ) of all elements of A , let P(1) denote the first element of P. Find the first element of P . Find the number of all such permutations P so that for all i,j ∈ A:

• if i<j<= P(1), then j appears before i in P; and
• if P(1)<i<j , then i appears before j in P

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