$(3+3+3)$ There are $6$ people. Lets call them $1,2,3,4,5$ and $6.$ Each of them has a hat. They

throw their hats in a box, and then each removes one hat from it $($each ordering equally likely$).$

Let $=$ number of people who get their own hat.

A pair of people is called a swapped pair if each has the other person$$s hat. $($There can be at most

three swapped pairs$)$

Let $=$ number of swapped pairs.

Compute the following.

a$)()$

b$)()$

c$)()$