We investigate the probability that a sample Γ=(Γ1,Γ2,…,Γn) of independent, identically distributed random variables with a geometric distribution has no elements occurring exactly j times, where j belongs to a specified finite `forbidden set' A of multiplicities. Specific choices of the set A enable one to determine the asymptotic probabilities that such a sample has no variable occuring with multiplicity b, or which has all multiplicities greater than b, for any fixed integer b≥1.