Question

Five cards are selected without replacement from a pack of 52 playing cards. What is the probability of exactly 3 hearts?

Answer 1

There are 13 total hearts in the deck, which leaves 39 non-hearts. You're drawing a hand of five cards, so the probability of getting exactly 3 hearts is

$\dfrac{\binom{13}3\binom{39}2}{\binom{52}5}=\dfrac{2717}{33320}$

as required.