I am a little bit confused about this problem. It said that three cards are dealt from a standard deck of cards. In how many ways can one get at least one king?
Now If I use the complement, then I want the number of ways one can deal 3 cards minus the number of ways of not getting a king. Well, 52*51*50 = 132600 is the number of ways of dealing 3 cards. The number of ways not dealing king is 48*47*46 = 103776. So I'd 132600 -103776 = 28824 ways of getting at least one king. Is this reasoning right?
On the other hand if I do $\binom{4}{1}\binom{48}{2} + \binom{4}{2}\binom{48}{1} + \binom{4}{3}\binom{48}{0}$, I get a different answer. Am I doing something wrong?