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We study the question on average and typical values of sums of pairwise Hamming distances for subsets of vertices of the  n -dimensional unit cube. We suggest an approach to the problem of evaluation of average and typical values of arbitrary functionals defined on subsets of a finite set as the sum of values assigned to ordered pairs of elements of this set; general formulas for this case are obtained. We find average and typical values of sums of pairwise distances in the case of all subsets of vertices of the  n -dimensional unit cube and of sums of pairwise distances for subsets of vertices of fixed cardinality.

On average and typical values of sums of pairwise distances for subsets of vertices of the n -dimensional unit cube