Covariance of Binomial Random Variables

[Obraz35]

Homework Statement

Let X be the number of 1's and Y be the number of 2's that occur in n rolls of a fair die. Find Cov(X, Y)

Homework Equations

Cov(X,Y) = E(XY) - E(X)E(Y)

The Attempt at a Solution

Both X and Y are binomial with parameters n and 1/6. Thus it is easy to find E(X) and E(Y), but for some reason finding E(XY) is really tripping me up. How does one go about finding expected values of products of binomial variables?