Not sure how to set this up, help with that would be much appreciated:
Barbra is interviewing ten candidates for a position. As she interviews candidates, she can determine their relative rank but not their true rank. For example, if there are 5 candidates and their true rank is 4, 2, 5, 1, 3 and she has interviewed the first three, she would rank them 2, 1, 3. She interviews the candidates one at a time, and after each interview she must either offer the candidate the position or reject him. Once she rejects a candidate he is lost forever. She wants to decide on a strategy for deciding when to stop and accept a candidate that will maximize the probability that she gets the best candidate. Assume the candidates arrive in random order.
(a) What is the probability that she gets the best candidate if she chooses the first one she interviews?
(b) What is the probability that she gets the best candidate if she interviews all of the candidates?
(c) Suppose there are only three candidates and she follows the following strategy. She rejects the first candidate and then selects the next candidate that is better than those already interviewed?