You are dealt a hand of 5 cards from a normal deck of cards. In how many ways could you be dealt at least 4 hearts?
I was working on this problem as part of a multiple choice quiz and was stumped by the available options. I thought this was a simple problem involving just choosing 4 hearts of the 13 hearts available and then multiplying that by the 48 remaining cards, yielding 34320, but the answer key claims it's in fact 29172. What is it that I'm missing here?