3. For which poker hand is there 13xC(4,2)x12xC(4,2)x44/2! possibilities?
If we consult the table of poker hands, we see that it is the number of 2 pairs. we can tell this by the fact that the two factors of C(4,2) indicate that there will be two pairs. The 13 is the number of ranks for the first pair, the 12 is the number of ranks for the second pair, the 44 is the number of cards left in the deck after getting the two pairs together which will not fill in a full house, and the 2! is there because the 2 pairs are 2 indistinguishable elements in the hand.