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A133227

The number of ways of selecting an ordered pair of permutations {P_1,P_2} out of S={1,2..,n} (i)each of length floor function {n/2} (ii)each element of P_1 is less than corresponding element of P_2 (iii) There are no common elements between P_1 and P_2.

Select a permutation of length k=floor function{n/2} from a set {1,2...,n). construct a cuboid-1 in k-th dimension. Without replacement find another permutation of same length and construct cuboid-2. Cuboid-1 can be kept within cuboid-2.