Can't get the solution to a question on combinations. From a standard deck of cards how many 5 card hands are possible consisting of b. two cards of one kind and three of another(like a full house). Is part a ^{13!}/_{9!4!}? part b not sure. Thanks! Hi, You have part a almost correct. ^{13!}/_{9!4!} is the number of ways of choosing 4 cards from the 13 hearts in the deck. But you want a 5 card hand with exactly 4 hearts. Thus you can select the final card from the 39 that are not hearts. Hence the number of 5 card hands with exactly 4 hearts is For part b you can select the first kind in 13 possible ways. From the 4 cards of that kind select 3, which you can do in ^{4!}/_{3!1!} ways. Thus far you have Now choose one of the 12 kinds rremaining and select 2 of the 4 cards of that kind. That you can do in Hence there are Penny
