Exercise $2.$ Let the size of the hash table be $m.$ Show that if a set of elements $S$ has a size $|S|>m*n$ for an integer $n,$ then there is a subset of $S$ with at least $n$ elements that all will be hashed to the same cell, no matter what hash function we use.

$[9$ points$]$

If separate chaining collision resolution strategy is used, what would be the average runtime of an insertion operation?

$[1$ point$]$