The Best Prize Problem Suppose that we are to be presented with $n$ distinct prizes,in sequence. After being presented with a prize, we must immediately decide whether to accept or reject it and consider the next prize. The only information we are given when deciding whether to accept the prize is the relative rank of that prize compared to ones already seen. That is, for instance, when the fifth prize is presented, we learn how it compares with the four prizes we’ve already seen. Suppose that once a prize is rejected, it is lost, and that our objective is to maximize the probability of obtaining the best prize, assuming that all $n!$ orderings of the prizes are equally likely. I have no idea how to go about this question, help me out.

This is the _secretary problem_. The Wikipedia article gives a proof showing that, with the best strategy, the probability of picking the best prize is at least $1/\mathrm e\approx 0.368$.