The Secretary Problem with Optimal Assignment

We consider the secretary problem with assignment of the applicants to m positions to be staffed in order to maximize the probability that we select only the m best, and assign the kth best to the kth position. A simple strategy is proposed. Although the optimal strategies for m = 1, 2 are known to be simple, we show that the optimal strategy for m = 3 is not necessarily simple. However, a simple strategy turns out to be a fairly good suboptimal strategy.