3 cards are chosen at random from a standard 52-card deck. What is the probability that they form a pair? (A 3-card hand is a 'pair' if two of the cards match in rank but the third card is different. For example, 668 is a pair, but 999 is not.)

THANKS FOR ALL HELP

ps the answer is not 48/425

alskdj Jan 30, 2019

#1**+3 **

I think this might be correct....but....I'd like someone else to check since I'm not great at these "counting" problems!!!

We have 13 ranks and we want to choose any 2 of 4 cards in one of them.....so.....number of possible pairs =

13 * 4C2

And...from any of the remaining 12 ranks, we want to choose any 1 of 4 cards from one of them =

12* 4C1

And the number of possible hands = 52C3

So..the probability is

[13 * 4C2] * [ 12 * 4C1] / 52C3 = 72 /425

CPhill Jan 30, 2019