How Many Ways to Make a Pair Given Five Poker Cards I'm confused at the general method of solving this type of problem.  The wikipedia page says that there are:
${13 \choose 1} {4 \choose 2} {12 \choose 3} {4 \choose 1}^{3}$ ways to select a pair when 5 cards are dealt.  Can someone outline what each calculation means?  For example, is $13 \choose 1$ the process of selecting 1 card in the beginning?

$13\choose 1$ is the number of ways of choosing the denomination of the pair, whether it is a pair of kings, or a pair of threes, or whatever.  Then there are $4\choose 2$ ways to choose suits for the two cards of the pair.
Then there are $12\choose 3 $ ways to choose the three different denominations of the remaining three cards from the twelve that are different from the denomination of the pair.  Each of those other three cards can be of ${4\choose 1}=4$ different suits, for ${4\choose 1}^3$ choices of three suits in all.
