Results 1 to 2 of 2

Thread: Committee Seating permutation problem

  1. #1
    Apr 2008

    Committee Seating permutation problem

    A committee has two presidents, two vice presidents, and two secretaries. In how many distinct ways can they sit around a circular table? Each office-holder must face across the table a person who holds a different office. This means one president cannot sit across from another president, etc. Assume that members of the same office are indistinguishable.

    I began by finding the total number of arrangements, which I *think* is 120/(2!2!2!) which is a circle permutation for 6 objects divided by 2! three times because the three offices have 2 members each that can be switched around to produce the same thing. But now that I think about it I could also switch the presidents AND vp's or even all of the members.

    Then, finding the number of ways we can make it so at least one office sits across from each other, there's 2 ways we can have all 3 pairs matched up, and if we have 2 pairs matched up there has to be 3 matched up. If we want only one pair matched up there are 2 ways to do it for the presidents matched up, 2 ways for the vp's and 2 ways for the secretairs. So I took 15-2-2-2-2 and got 7. However when I drew it out I have at least 8! Any thoughts?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Eater of Worlds
    galactus's Avatar
    Jul 2006
    Chaneysville, PA
    Remember, arrangements around a circle are (n-1)!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Seating Problem - Any ideas?
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: Sep 22nd 2010, 11:06 PM
  2. one more committee problem
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: May 13th 2010, 03:05 PM
  3. Seating arrangements problem
    Posted in the Statistics Forum
    Replies: 0
    Last Post: Nov 8th 2009, 04:08 PM
  4. Seating Arrangement Problem
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: Dec 4th 2007, 12:45 PM
  5. seating problem
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: Nov 20th 2007, 05:17 PM

Search Tags

/mathhelpforum @mathhelpforum