The paper considers sampling with replacement of equiprobable groups of a fixed size m from a finite population S. Given a subset AℝS, the distributions of (a)the number of distinct elements of A in a sample of size k and (b)the sample size necessary to obtain at least say n elements of A are given. Neat formulas are given especially for the expected values of these, as well as some related random variables. Further, an optimal strategy is derived to collect all elements of S under the assumptions that sampling one group costs α monetary units and that it is possible to purchase the elements which are missing at the end of the sampling procedure at a price of β>α/m per element.
