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Find the number of all such permutations P

Source: BStat-BMath 2017: Problem 7

May 14, 2017

number theorycountingcombinatoricscontests

Problem Statement

Let

A=\{1,2,\ldots,n\}

. For a permutation

P=(P(1), P(2), \ldots, P(n))

of the elements of

A

, let

P(1)

denote the first element of

P

. Find the number of all such permutations

P

so that for all

i,j \in A

:
(a) if

i < j<P(1)

, then

P

appears before

i

in

P

; and
(b) if

P(1)<i<j

, then

i

appears before

j

in

P

.

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