Probability of making a full house in a poker hand 

We need to have a three of a kind and a pair. We could have a three of a kind in 
\[{13 \choose 1} {4 \choose 3}=13\times 4=52 \text{different ways}.\]
Next we want to get a pair from the remaining 12 kinds of cards 
\[{12 \choose 1}{4 \choose 2}=12\times 6 =72  \text{different ways}.\]
So we can get a full hourse in 
\[52 \times 72   \text{different ways}.\]
The total number of ways one can choose 5 cards out of 52 cards is 
\[{52 \choose 5}=2598960.\]
So the probability of a full house is
\[\frac{52 \times 72}{2598960}= 0.00144057623.\]