Probability of 3 cards having the same denomination:
(There are 13 ways we can get 3 of a kind).
The probability that the next 2 cards are a pair: 
(There are 12 ways we can get a pair, once we have already got our 3 of a kind).
The number of ways of getting a particular sequence of 5 cards where there are 3 of one kind and 2 of another kind is:
So the probability of a full house is
Number of ways of getting full house:
Number of possible poker hands 
full house 
