What is the probability of drawing two aces, two kings, or an ace and a king?

Question

A person removes 2 aces and a king from a deck of 52 playing cards, and draws, without replacement, two more cards from the deck. Find the probability that the person will draw two aces, two kings, or an ace and a king (in either order)

Answer 1

P(2 Aces) = (2/49)(1/48) = 2C2 / 49C2 = 1/1176

 

P(2 Kings) = (3/49)(2/48) = 3C2 / 49C2 = 1/392

 

P(A,K) = 2C1•3C1 / 49C2 = 1/196 

 

Add up these three distinct probabilities to answer the question.