22. Avril has certain standards for selecting her future husband. She has n suitors and knows how to compare any two and rank them. She decides to date one suitor at a time randomly. When she knows a suitor well enough, she can marry or reject him. If she marries the suitor, she can never know the ones not dated. If she rejects the suitor, she will not be able to reconsider him. In this process, Avril will not choose a suitor she ranks lower than at least one of the previous ones dated. Avril’s goal is to maximize the probability of selecting the best suitor. To achieve this, she adopts the following strategy: For some m, 0 ≤ m dumps the first m suitors she dates after knowing each of them well no matter how good they are. Then she marries the first suitor she dates who is better than all those preceding him. In terms of n, find the value of m which maximizes the probability of selecting the best suitor. Remark: This exercise is a model for many real-world problems in which we have to reject “choices” or “offers” until the one we think is the “best.” Note that it is quite possible that we reject the best “offer” or “choice” in the process. If this happens, we will not be able to make a selection.