The following is the total number of 5-card poker hands drawn from a standard deck of 52 cards. The number of possible 5-card poker hands would then be the same as the number of 5-element subsets of 52 objects.
The only difference is the order in which the cards are dealt. Thus the following three examples point to the same poker hand. Usually the order in which the cards are dealt is not important (except in the case of stud poker). Thus this is primarily a counting exercise. three of a kind) is the number of possible hands for that type over 2,598,960. The probability of obtaining a given type of hands (e.g. Thus the probability of obtaining any one specific hand is 1 in 2,598,960 (roughly 1 in 2.6 million). There are 2,598,960 many possible 5-card Poker hands. Working with poker hands is an excellent way to illustrate the counting techniques covered previously in this blog – multiplication principle, permutation and combination (also covered here). The discussion is mostly mathematical, using the Poker hands to illustrate counting techniques and calculation of probabilities
This post works with 5-card Poker hands drawn from a standard deck of 52 cards.
