The author previously obtained a strong law of large numbers for combinatorial sums ∑iXniπn(i), where ∥Xnij∥ is an n-order matrix of random variables with finite fourth moments and (πn(1), πn(2), …, πn(n)) is a random permutation uniformly distributed on the set of all permutations of numbers 1, 2, …, n, independent from the random variables Xnij. No mutual independence of elements of the matrix is assumed. We derive the combinatorial SLLN under more general assumptions in the present paper and discuss the behavior of rank statistics.