I'm dealing with an exercise which deals with the poker game. I need to calculate the probability of getting a full house.
Full house is getting 3 cards of the same type and 2 cards of the same type.
I've made a research, but I cannot understand why the combination for getting a full house is
$13 \choose 1$$4 \choose 3$$12 \choose 1$$4 \choose 2$ Can someone explain me in details why we multiply those combinations? I mean, explain why we consider these numbers.