Results 1 to 2 of 2

Math Help - Combinatorics

  1. #1
    Newbie
    Joined
    Nov 2006
    Posts
    4

    Combinatorics

    Hello I am in need of urgent help with a problem that involves permutations. The question goes as follows:

    The Northeastern University College of Computer and Information Science has 5 women and 20 men who are full-time faculty members. Their photos are to be displayed in a single row at the entrance to their building.

    iii. In how many ways can the photos be displayed so that no two women are adjacent? Hint: Consider arranging the men’s photos first and then placing the women’s photos among the men’s photos so as to ensure that no two women are adjacent.

    I'm not sure where to start on this one, any help would be greatly appreciated. Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,738
    Thanks
    645
    Hello, checkeredshawn!

    The Northeastern University College of Computer and Information Science
    has 5 women and 20 men who are full-time faculty members.
    Their photos are to be displayed in a single row at the entrance to their building.

    (iii) In how many ways can the photos be displayed so that no two women are adjacent?
    Hint: Consider arranging the menís photos first and then placing the womenís photos
    among the menís photos so as to ensure that no two women are adjacent.

    That hint tells the whole story . . .

    Place the 20 men's photos in a row. .There are 20! ways.

    Leave a space between the men's photos and on the ends.
    . . _ M _ M _ M _ M _ ... _ M _ M _ M _

    To place the women's photos, we choose 5 of the available 21 spaces.
    . . There are: . P(21,5) \,= \,\frac{21!}{16!} ways.


    Therefore, there are: . 20! \times \frac{21!}{16!} ways.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Combinatorics.
    Posted in the Discrete Math Forum
    Replies: 16
    Last Post: July 20th 2010, 02:29 AM
  2. Combinatorics
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: June 18th 2010, 08:14 PM
  3. Combinatorics
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: June 3rd 2010, 05:24 PM
  4. combinatorics
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 1st 2010, 10:53 PM
  5. Combinatorics
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: October 10th 2009, 06:03 AM

Search Tags


/mathhelpforum @mathhelpforum