In a fivecard poker hand what is the probability of a full h

In a five-card poker hand, what is the probability of a full house, with three-of-a-kind and two-of-a-kind?

Solution

Pick a type of card: 13 ways
Pick 3 of that type of card: 4C3=4 ways

Pick a different type of card: 12 ways
Pick 2 of that type: 4C2=6
# of \"full-house hands\" = 13*4*12*6=3744
# of 5 card hands: 52C5=2598960
Prob(full house)= 3744/2598960=0.00144057