Finitely many urns are filled with balls each having one of the labels 1,...,N is known proportions. Balls can be drawn with replacement from any urn at the cost of c>0 monetary units per drawing. Let Xk be the number of labels that show up in the first k drawings. The paper solves the problem to find a selection rule for the urns to be used and a stopping rule such that E(XÅτ-cτ) is maximized. A second problem of this kind is also treated.
