Counting five-card poker hands. 0 about this question refers to a standard deck of playing cards. if you are unfamiliar with playing cards, there is an explanation in "probability of an event" section under the heading "standard playing cards." a five-card hand is just a subset of 5 cards from a deck of 52 cards. (a) how many different five-card hands are there from a standard deck of 52 playing cards? solution there are (3) ways to select a subset of 5 cards from a set of 52 cards. (b) how many five-card hands have exactly two hearts? solution there are (1) ways to select a subset of 2 hearts from the set of 13 hearts in the deck. there are ways to select a subset of 3 non-hearts from the set of 39 non-hearts in the deck. since the hearts and the non-hearts must all be selected in order to determine the cards in the hand, the product rule applies, and there are a total of ways to select a 5-card hand with exactly two hearts. how many five-card hands are made entirely of hearts and diamonds? (d) how many five card hands have four cards of the same rank? le) a "full house" is a five-card hand that has two cards of the same rank and three cards of the same rank. for example, (queen of hearts, queen of spades, 8 of diamonds, 8 of spades, 8 of clubs). how many five-card hands contain a full house? how many five-card hands do not have any two cards of the same rank?