How many 5 card hands would have only hearts?

Answer 1

1287

There are thirteen hearts. Order doesn't matter -- so you need to know how many combinations of five cards you can choose from 13. The binomial coefficient gives you the answer:

Combin(13,5) = 13!/[(5!)*(13-5)!) = 1287

You can use the COMBIN function in Excel to get this.

Answer 2

Assuming a standard 52 card deck, there are 13!/(5!*(13-5)!) = 1287 sets of 5 hearts. It is not simply 13*12*11*10*9 because the order of the cards in the hand is irrelevant.