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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

 Jan 30, 2019
edited by alskdj  Jan 30, 2019
 #1
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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

 

 

cool cool cool

 Jan 30, 2019

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