Binomial Coefficient/Examples/Number of Bridge Hands

Theorem
The total number $N$ of possible different hands for a game of bridge is:
 * $N = \dfrac {52!} {13! \, 39!} = 635 \ 013 \ 559 \ 600$

Proof
The total number of cards in a standard deck is $52$.

The number of cards in a single bridge hand is $13$.

Thus $N$ is equal to the number of ways $13$ things can be chosen from $52$.

Thus: