Let L(n,k,k,t) denote the minimum number of k-subsets of an n-set such that all the (nk) k-sets are intersected by one of them in at least t elements. In this article L(n,k,k,2) is calculated for infinite sets of n's. We obtain L(90,5,5,2) = 100, i.e., 100 tickets needed to guarantee 2 correct matches in the Hungarian Lottery. The main tool of proofs is a version of Turán's theorem due to Erdös. © 1996 John Wiley & Sons, Inc.