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no of permutations of 1,2,..., n with s_i > s_j$ for all i >= j + 3 when n =5, 7

Source: 2013 Saudi Arabia Pre-TST 4.3

September 13, 2020
combinatoricspermutation

Problem Statement

How many permutations (s1,s2,...,sn)(s_1, s_2,...,s_n) of (1,2,...,n)(1,2 ,...,n) are there satisfying the condition si>sjs_i > s_j for all i≥j+3i \ge j + 3 when n=5n = 5 and when n=7n = 7?
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