Results 1 to 2 of 2

Math Help - permutations and combinations

  1. #1
    Newbie
    Joined
    Jun 2011
    Posts
    3

    permutations and combinations

    I ran into this problem:

    You are choosing 5 teams out of a group of 23 people. You do this by choosing a team lead for each team, and then letting the team leads choose their teams in round-robin fashion. You choose the order in which the round-robin selection goes at random. Each team lead is guaranteed to pick the most-desirable unpicked person each time, and it turns out everyone has the same priorities as to who they would pick, so the competition is likely to be stiff. How many possible outcomes are there? Outcomes are the "same" only if they have exactly the same lead+team arrangements.

    I know it has to do with permutations, but I have no idea how to solve it.

    Any help will be appreciated
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by andyandy26 View Post
    I ran into this problem:

    You are choosing 5 teams out of a group of 23 people. You do this by choosing a team lead for each team, and then letting the team leads choose their teams in round-robin fashion. You choose the order in which the round-robin selection goes at random. Each team lead is guaranteed to pick the most-desirable unpicked person each time, and it turns out everyone has the same priorities as to who they would pick, so the competition is likely to be stiff. How many possible outcomes are there? Outcomes are the "same" only if they have exactly the same lead+team arrangements.

    I know it has to do with permutations, but I have no idea how to solve it.

    Any help will be appreciated
    Once the team leads have been chosen which member is chosen in each round is fixed, only their order varies.

    so there are:

    TL=\frac{23!}{18! 5!}

    ways of choosing the team leads (ignoring order)

    Then for any selection of leads there are 5! arrangements of persons in each round except the last where there are 60 arrangement

    Then the required answer is the product of all these.

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Permutations and combinations?
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: September 15th 2010, 09:12 PM
  2. DNA permutations and combinations
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: July 8th 2010, 02:45 PM
  3. Permutations and Combinations Help!
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: November 25th 2009, 06:38 PM
  4. combinations of permutations?
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: November 10th 2009, 06:21 PM
  5. Permutations and Combinations
    Posted in the Statistics Forum
    Replies: 1
    Last Post: January 27th 2009, 03:27 AM

Search Tags


/mathhelpforum @mathhelpforum