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You are dealt 6 cards and find you have four 5s plus two other cards. You put those two non-scorers in the crib. You hope for a ten on the turn-up, but it's an off card that doesn't help anything. How do you score the 5s?

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You have 6 pairs (CD,CH,CS,DH,DS,HS), and 4 ways to make 15 (CDH,CDS,CHS,HDS), for a total of 20 points.

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    For what it's worth, you can count the pairs with the binomial coefficient: "4 choose 2" (because it takes two to make a pair). Likewise, you can count the 15's with "4 choose 3".
    – The Chaz 2.0
    Jul 10, 2014 at 16:49

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