Recreational Math

Card and Dice Games

What are the possible numbers of distinct 5-card hands in 5-card poker and 13-card hands in bridge?

There is, of course, a mathematical way of determining the possible number of distinct 5-card hands in poker—or the various combinations of 5 cards from a 52-card deck. The formula, in which N is the number of combinations, is as follows (note: the 52 written over 5 is called a binomial coefficient; for more about coefficients, see “Algebra”):


Not to be outdone, such a number can be determined for bridge games, too. In the following, N again represents the combinations:



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