Expected number of collisions while distributing balls in boxes

HINT

Yes. Whenever you are asked to find an expected value, always check to see if you can use the linearity of expectations. Remember that linearity of expectations apply even when variables are dependent!

For any pair $i < j$, let $X_{ij}$ be the indicator variable for whether $(i,j)$ is a colliding pair.

• What is $E[X_{ij}]$?

• How many pairs are there?

• Use linearity of expectation...

Lemme know if you need further help.