Optimal Selection of the K Best of a Sequence with K Stops

We first consider the situation in which the decision-maker is allowed to have five choices with purpose to choose exactly the five absolute best candidates from N applicants. The optimal stopping rule and the maximum probability of making the right five-choice are given for large N a N, the maximum asymptotic value of the probability of the best choice being limN-00P(win)~0.104305. Then, we study the general problem of selecting the k best of a sequence with k stops, constructing first a rough solution for this problem. Using this suboptimal solution, we find an approximation for the optimal probability values Pk of the form [formula] for any k = N