text: Most of the answers you're getting are too big.  They count A♥A♦ as distinct from A♦A♥.  It's the difference between permutations, where order matters, and combinations, where it doesn't.\n\nThere are 4C2 = 6 ways of picking 2 aces from 4, and 48 ways to pick the 3rd card.  So top of the fraction is 288.\n\nThere are 52C3 = 22,100 ways to pick any 3 cards, and that's the bottom of the fraction.  Divide top and bottom by 4 to simplify.  You get 72/5525.\n\nWith card hands it's easy to count the same hand twice.  8's and aces is the same as aces and 8's.  Besides being valedictorian at Las Vegas High School in '64, some of my family is in the business.