In a poker tournament they combine two 52card decks How many

In a poker tournament, they combine two 52-card decks. How many full-house 5-card hands are possible in such a game?

Solution

A full has has a three of a kind and a pair. So, two ranks are involved.

There are 13 ranks in which you can choose a three of a kind. In each rank, there are 4C3 = 4 ways to choose 3 cards.

There are 12 remaining ranks to choose the pair from. In each rank, there are 4C2 = 6 ways to choose a pair.

Thus, there is a total of 13*4*12*6 = 3744 full houses. [ANSWER]