{A,2,3,4,5,6,7,8,9,10,J ,Q ,K} and four suits – {Hearts, Diamonds, Spades, Clubs} . A Hand is a set of 5 cards picked up from the standard deck. How many different hands contain at least one of the following two cards : {K of Hearts, Q of Diamonds} ?
I'm having a little trouble finding the answer to this problem. I know that since two cards out of 5 have to be certain cards, that the choices for the other 3 cards is C(50,3). I also know that there are C(52,5) choices of possible hands for a deck of cards. However, I'm not sure what I would do if I needed to count the total number of hands containing the specified cards, but I'm thinking it would contain some sort of indirect counting method
Best Answer
Hint
You already know that there are $C(52,5)$ choices of possible hands for a deck of cards in total
How many possible hands include neither the King of Hearts nor the Queen of Diamonds?