Barbara is interviewing $9$

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 them. Once she rejects a candidate they are 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.