Yahoo Answers: Answers and Comments for Math12 Combinatorics? [Mathematics]
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From Anonymous
enCA
Tue, 04 Aug 2009 20:06:21 +0000
3
Yahoo Answers: Answers and Comments for Math12 Combinatorics? [Mathematics]
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From powlen: 9*10^3*25^2 = 5,625,000  recommend...
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https://ca.answers.yahoo.com/question/index?qid=20090804200621AAzic3m
Wed, 28 Dec 2016 12:37:47 +0000
9*10^3*25^2 = 5,625,000  recommendations: There are 9 alternatives for the 1st quantity, 10 alternatives for all of the subsequent 3 numbers, and 25 alternatives for all of the two letters.

From ej: Let's try to simplify and then build the a...
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https://ca.answers.yahoo.com/question/index?qid=20090804200621AAzic3m
Tue, 04 Aug 2009 22:59:40 +0000
Let's try to simplify and then build the answer up.
Here's how I reason:
There are 4 aces in the deck, so there are 4 ways I could pick the first one, and after that there are three other aces I could draw to get my second ace. Because I don't care what order they come in, I divide by two for the two possible orderings of two cards. This is "n choose r" or C(n, r) = n! / ((r!)(nr)!) = 4! / ((42)! (2!)) = 24 / (2 * 2) = 6 (You can verify this one on your fingers.)
Now, for a pair of aces and kings, there are essentially also 6 ways I could draw a pair of kings. Since it doesn't matter whether I got these 4 cards as AAKK, AKAK, AKKA, KAKA or whatever, without regard to order, there are 36 ways I can be holding a pair of kings and aces.
But we're not just interested in aces and kings, it's aces and another pair. After you have a pair of aces, there are 12 other ranks you could get a pair of. And since there are 6 ways to hold any particular pair, I think the number of ways you can hold Aces and another pair is: 6 * 6 * 12.
Now, for each combination of those 4 cards, there are 48 other cards that can make up your 5th card (some of which will form a full house, and some of which don't  see below).
So, all told, I think the answer is 6 * 6 * 12 * (524) = 20736
If you mean hands with a pair of aces, another pair, and the 5th card strictly not matching either pair, then it's 6 * 6 * 12 * (528) = 19008.