Consider a population π composed of speciesin propotions p1,....pkrespectively. The population is searched by selecting a group of m randomly chosen members at a time.Let dm(n) denote the number of distinct species discovered in n selections.At stage n a reward offeris available to us where c > 0 is a fixed cost associated with each selection and h is a known, nondecreasing function defined over the set of positive integers. We wish to determine the time at which it is optimal to conclude the search. Some optimal and adaptive strategies are proposed.