Suppose we have a hash table of size n. Given an element to add to a hash table, a good hash function will place that element in any one of the table entries with probability 1. We want to avoid collisions. Let us examine this problem a little more closely in this question. Suppose we have n containers C1,., Cn (which represent the table entries) and we throw n balls Bi,..., Bn (which represent the elements) into the containers with a uniform distribution. That is, the probability that a ball falls in a particular container is 1. Let Xi be the number of balls that falls in Ci (a) Show that Pr(Xi 2k)