Probablity: A pinochle deck consists of 48 card, 2 of each of the 9 through the ace in 4 suits. If 2 cards are drawn at random, what is the probability that both will be black or both will be kings?

Question

Schoolwork, I can't figure this out, but I'd like to know how I could solve it

Answer 1

The Probability of 2 Black is ₂₄C₂/₄₈C₂ (24 black cards choose 2) and 2 Ks is ₈C₂/₄₈C₂ (8 kings choose 2) but the tricky part is that we have to remove all double counting which happens when 2 black kings are picked which happens ₄C₂/₄₈C₂

So the solution should be (24*23 + 8*7 - 4*3)/(48*47)