Please help with parts (b), (d), and (e)!

The problem is to determine the expected maximum size M of keys in a hash table of size n with n keys. The objective is to show that E[M] is O(clogn/loglogn). This is done in the following parts. (a) [0 pt] Don't do this part, but read it. This is straight forward since the probability of a key being in a particular slot is 1. (b) [1 pt] Do this part. Show Pk, the probability that the slot containing the most keys has k keys, is at most nQk (c) [0 pt] Don't do this part, but read it. Using Stirling's approximation, we can show Qk1 and N such that for nN,Qk0