The number of matches approximately obeys a Poisson probability law. Consider the number of matches obtained by distributing M balls, numbered 1 to M, among M urns in such a way that each urn contains exactly 1 ball. Show that the probability of exactly m matches tends to e-1(1/m !), as M tends to infinity, so that for large M the number of matches approximately obeys a Poisson probability law with parameter 1.