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{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

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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?

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