Answered Question

ankitgu

M$1 May 02, 2009 10:32 PM

Statistics question about a game of bridge.

There are 4 players, 2 teams of two players each, and a standard 52 card deck, and each player gets 13 cards.

The number of bridge games is equal to (52C13)*(39C13)*(26C13)*(13C13 = 1) according to an answer key I have.

In another question, we had to find the probability of a single player getting all the spades, which is 4*(39C13)*(26C13)*(13C13 = 1) divided by answer from previous question. We multiply by four because we can choose between 4 players for getting all the spades.

Here's my question - why don't we account for there being 4 players in the total number of games possible like we did in the problem about the spades? Combinations inherently don't care about order, but doesn't it create for a different game from the point of view of a specific player if the cards were in different hands? I've confused myself a little bit here, but just want to know why we multiplied by 4 in one of those and not the other.

Interesting Question? Yes (0) No (0)

RSS

Best Answer Chosen by Asker

rickg

May 03, 2009 12:30 AM

In the first case, you *are* taking into account rotations of the hands around the table. Start with player 1 (is that East? Not a bridge player). If you pull 13 cards out of the deck randomly for that player, there are 52C13 possible hands (which are really *all* the possible 13 card hands for a 52 card deck). Then move to player 2 and pull 13 cards from the 39 remaining; that's the 39C13. And proceed for the last 2 players. If you think about it a little, you should see that we've counted every possible game, including "rotations", where the hands are all the same but rotated around the board.

In the second case, you basically pull all the spades out of the deck, leaving a deck of 39. Then hand that hand to player 1, leaving 39C13 for player 2, 26C13 for player 3, and 1 for player 4. But players 2-4 never got the all-spades hand when counting those up, so you have to hand the all-spades hand to the other players in turn, and count the same set of possibilities for the others. Thus the 4.

Does that make sense?

Asker's Rating:

• That makes perfect sense - that 52C12 in the first case gets all the possible hands from the 52 card deck. In the case of the spades being pulled out, it doesn't.

Thanks for answering that so quickly and making it easy to understand :)

I think I've done the right thing on this so that you get the tip, we'll find out shortly though... still new to this.

Helpful Answer?

(0)

(0) Tip rickg for this answer

Permalink | Report

Answer this Question

Ask a Question

Top of Page

Buy Mahalo Dollars with Credit Card or PayPal

Top Members

This Week All Time

buddawiggi
2nd Degree Black Belt
25027 Points
M$701.03 Earned
cfinke
2nd Degree Black Belt
23219 Points
M$29.75 Earned
unwirklich
Purple Belt
2323 Points
M$131.55 Earned

See All

Most Popular Tags

mahalo(1398)

twitter(923)

iphone(449)

music(435)

google(324)

food(290)

internet(283)

beer(267)

online(266)

money(246)

apple(239)

movies(235)

aotd(233)

facebook(228)

answers(203)

video(197)

health(197)

free(190)

windows(190)

dog(188)

See All

Welcome New Members

yuki0, November 11, 2009 05:10 PM
ngettman, November 11, 2009 05:09 PM
michaelus, November 11, 2009 05:06 PM
domsky, November 11, 2009 04:56 PM
habitissimo, November 11, 2009 04:54 PM

Mahalo Dollars are the currency of Mahalo Answers.

Each Mahalo Dollar costs $1.

Once you earn more than 40 Mahalo Dollars, you can request to be paid via PayPal. Each Mahalo Dollar is currently worth $0.75 when paid out via PayPal. Learn More