Results 1 to 2 of 2

Math Help - Bridge Probability Question/Inclusion, Exclusion

  1. #1
    Newbie
    Joined
    May 2009
    Posts
    5

    Bridge Probability Question/Inclusion, Exclusion

    Hello:

    How do we find the number of bridge hands that are weak in a suite (that is, lacking in either an ace, King or Queen) in a suite?

    Would we want to do the following:

    (1) find the number of hands that are lacking in a suite ->
    Say, the suite is hearts
    Since you have 52 cards, would you have then 52 - 3 cards to choose from.
    So you would have (49 choose 13) ways of choosing a hand that is lacking in hearts. Then, since there are (4 choose 1) ways to choose which suite to be lacking in, total you have 4 x (49 choose 13) ways for a hand to be lacking in a suite.
    (2) But then you have overcounted, and you must substract out the ones that are lacking in 2 suites, and then you have (46 choose 13) for those.
    (3) Then you must add back in those that are lacking in 3 suites:
    (2 choose 0) x (43 choose 13)
    (4) Then you must substract out the number that is weak in 4 suites, which is (3 choose 0)*(40 choose 13)
    (5) The next thing to do is to add back in the number that is weak in 5 suites, but that is impossible, and hence you are done.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,663
    Thanks
    1616
    Awards
    1
    Quote Originally Posted by bodensee9 View Post
    The next thing to do is to add back in the number that is weak in 5 suites, but that is impossible, and hence you are done.
    Try this out: \sum\limits_{k = 1}^4 {\left( { - 1} \right)^{k+1} \binom{4}{k} \binom{52-3k}{13}} .

    The last I played bridge there were only four suits.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Inclusion and exclusion question
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: April 19th 2011, 04:00 AM
  2. inclusion & exclusion question help
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 17th 2010, 07:49 AM
  3. inclusion/exclusion question
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: November 3rd 2009, 07:31 PM
  4. Probability Question using Inclusion-Exclusion Formula.
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: October 10th 2009, 07:30 AM
  5. Probability Inclusion Exclusion
    Posted in the Advanced Statistics Forum
    Replies: 11
    Last Post: January 21st 2008, 03:41 PM

Search Tags


/mathhelpforum @mathhelpforum