Permutations and Combinations

Question

In a standard deck of 52 playing cards, there are four suits (black spade, black club, red heart, red diamond), and 13 cards in each suit (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King).

If I draw 8 cards, what is the probability that all of them are red, and exactly 2 of them are hearts?

Answer 1

P(8 draws from 8 cards are all red and 2 are hearts) = P(a draw of 8 cards includes 6 diamonds and 2 hearts) =

C(13,6)*C(13,2)/C(52,8) = 1716 * 78/752538150 = 572/3215975 = 0.0001779