In this work we analyze a class of diminishing 2×2 Pólya-Eggenberger urn models with ball replacement matrix M given by M= &bigl;( -a   0 c  -d&bigr;), a,d∈&N; and c∈&N;0. We obtain limit laws for this class of 2×2 urns by giving estimates for the moments of the considered random variables. As a special instance we obtain limit laws for the pills problem, proposed by Knuth and McCarthy, which corresponds to the special case a=c=d=1. Furthermore, we also obtain limit laws for the well known sampling without replacement urn, a=d=1 and c=0, and corresponding generalizations, a,d∈&N; and c=0.