A generalization of the classical secretary problem

The classical secretary problem is a well known optimal stopping problem from probability theory. It is usually described by different real life examples, notably the process of hiring a secretary. Imagine a company manager in need of a secretary. Our manager wants to hire only the best secretary from a given set of n candidates, where n is known. No candidate is equally as qualified as another. The manager decides to interview the candidates one by one in a random fashion. Every time he has interviewed a candidate he has to decide immediately whether to hire her or to reject her and interview the next one. During the interview process he can only judge the qualities of those candidates he has already interviewed. This means that for every candidate he has observed, there might be an even better qualified one within the set of candidates yet to be observed. Of course the idea is that by the time only a small number of candidates remain unobserved, a recently interviewed candidate that is relatively best will probably also be the overall best candidate.