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( 3 + 3 + 3 ) There are 6 people. Lets call them 1 , 2 , 3 , 4 , 5 and 6

(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 x= 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 Y= number of swapped pairs.
Compute the following.
a)E(x)
b)E(Y)
c) Var(x)
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