Hey guys, homework problem on expectation. This is what i have so far.

Suppose a fair die is rolled ten times. Find numerical values for the expectations of:

1) the number of faces which fail to appear in the ten rolls

Here's what i got:

$\displaystyle E(x) = \sum x P(X = x) = 1 P(X = 1) + 2 P(X = 2) + ... + 5 P(X = 5) $

So the probability that x faces dont is ... this is the part im not sure about.

$\displaystyle P(X = x) = ?$

I know, for example, that $\displaystyle P(X = 5)$ would have to be (1/6)^10

After this i am unsure how to proceed. $\displaystyle P(X = 1)$ seems like it would NOT be $\displaystyle \left(\begin{array}{cc}10\\5\end{array}\right)(5/6)^{10}$ ... I cant figure out how to find a general formula for this.

Thanks in advance!