Computer Science Canada Math Help - DATA |
| Author: | RyanHB [ Thu Sep 23, 2010 6:42 pm ] |
| Post subject: | Math Help - DATA |
This is the question - A bridge Hand consists of 13 cards. How many bridge hands include 5 cards of one suit, 6 cards of a second, and 2 cards of a third. Deck has 52 cards btw. It's so simple, but after transitioning to university, I lost all data knowledge..ANy help? BTW the answer is 4 billion something.. The books gives us the answer, but I forget how to do this.. |
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| Author: | TheGuardian001 [ Thu Sep 23, 2010 8:46 pm ] |
| Post subject: | Re: Math Help - DATA |
I believe (I never was great at this, even when I knew it, so I may be way off) that the you need to do something like this ((13 choose 6)*4) * ((13 choose 5)*3) * ((13 choose 2)*2) 13 choose N will get you the number of combinations of N cards in one suit. Multiplying that by the number of suits available (4 for the first, 3 for the second, since we exclude the one chosen by the first, and so on) gets you the total combinations per N cards. Multiplying all of those numbers together will get you the total number of combinations of all sets across all suits. I got 4 134 297 024 combinations, which seems like the right number. |
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