Suppose a die is rolled $14$ times, and $X$ be the number of faces that appear exactly 2 times. How can I find $E(X)$? It seems that this question is relatively straightforward as it resembles the binomial. However, I cannot complete the entire argument if I try to do it in accordance with $X=0$, $X=1$, and so on and then compute the probability of each. Does anyone have any ideas?

Just multiply the probability that some face occurs exactly twice (which can be calculated with the binomial distribution) with $6$, the number of faces. Here, we use that expectations are additive : $E(X+Y)=E(X)+E(Y)$
