Results 1 to 2 of 2

Math Help - Permutations of people

  1. #1
    Newbie
    Joined
    May 2009
    Posts
    4

    Permutations of people

    Hi all, I've got this question here... don't even know how to begin solving it.

    There are 28 people from 7 countries; 4 people from each country. I'm required to put them in a line, so that each person will have at least one neighbour from the same country. How many such orderings exist?

    Thanks in advance.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,712
    Thanks
    1642
    Awards
    1
    Quote Originally Posted by Aldarion View Post
    There are 28 people from 7 countries; 4 people from each country. I'm required to put them in a line, so that each person will have at least one neighbor from the same country. How many such orderings exist?
    Suppose that {a,b,c,d} is the set of people from country Q.
    Then there are three parings of the four people: (ab)(cd); (ac)(bd); (ad)(bc).
    Thus there are 3^7 ways to choose the paring of all 28 people.

    For any choice of parings, we have (14!) ways to arrange these pairs into a line.

    In each of those lines there are 2^{14} ways to arrange the couples.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. set of all people
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: October 16th 2011, 01:27 PM
  2. Replies: 2
    Last Post: July 24th 2011, 03:57 AM
  3. Replies: 1
    Last Post: February 14th 2011, 07:18 AM
  4. How many people can be fed?
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: August 29th 2010, 02:23 PM
  5. Permutations: People in Rooms
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: July 17th 2010, 10:07 PM

Search Tags


/mathhelpforum @mathhelpforum