aez-notes

We often read of someone who has been dealt 13 spades at bridge. With a well-shuffled pack of cards, what is the chance that you are dealt a perfect hand (13 of one suit)? (Bridge is played with an ordinary pack of 52 cards, 13 in each of 4 suits, and each of 4 players is dealt 13)

For a particular suit this is

\[ \prod_{i=0}^{12} \frac{13 - i}{52 - i} \]

and then there are four suits in which this can be achieved.

4 * product((13 - i) / (52 - i), i, 0, 12);