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combinatorics challenge

Started by trub May 18, 2003 at 6:26 PM 5 replies 1.1k views

Original Post

May 18, 2003 at 6:26 PM

Okay, this took me like 3hrs to do - so hopefully it will take you guys a bit to answer as well =) Using a standard deck of 52 cards, how many 13 card bridge hands can be had that have more spades than hearts, and at least 2 aces? I got 67,202,490,464 via inclution/exclusion with the following cases: c1 = no ace in the 13 card hand c2 = exactly one ace in the 13 card hand c3 = number of hearts in the hand is >= number of spades in hand I was happy with the answer for it it was less than the total combinations of C(52,13) and not negative =) Although, given its so hard to be sure, any input from you guys would be cool. NOTE: I''m not asking for homework help for I already have an answer, still - if you would rather me not ask such questions just let me know for future reference.

Zipster

511

Zipster

May 18, 2003 at 6:35 PM

I don''t play bridge, so I have no idea what to do

trub

Author

trub

May 18, 2003 at 6:41 PM

quote:
Original post by Zipster
I don''t play bridge, so I have no idea what to do

you don''t need to. You just need to know what makes up a regular deck of cards (4 suits, 13 cards each suit).

Punty50

May 18, 2003 at 8:25 PM

If you did your calculations right, I would agree with you, except how did you ensure that the aces condition was covered in C3. Well wait, you don''t have to

Seems to be a lot of work, so good job. I will do my own calculations and get back to you tomorrow during study hall.

Brendan

trub

Author

trub

May 19, 2003 at 7:22 AM

quote:
Original post by Anonymous Poster
Brute force says you''re right.

Do you mind me asking how you did it by brute force? All the possible combinations of 13 card hands is like ~600 billion, I thought that would take a while to churn through...

Thanks

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