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 a. exactly 4 hearts 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 39 x  13!/9!4! 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 13 x  4!/3!1! = 52 ways to select the first 3 cards. Now choose one of the 12 kinds rremaining and select 2 of the 4 cards of that kind. That you can do in 12 x  4!/2!2! = 72 ways. Hence there are 52 x 72 = 3744 5 card hands with two cards of one kind and three of another. Cheers, Penny Go to Math Central