Results 1 to 3 of 3

Math Help - Arrangements of Boys and Girls

  1. #1
    Member
    Joined
    Jul 2009
    Posts
    132

    Arrangements of Boys and Girls

    How many ways can 4 different boys and 4 different girls be arranged in a line if
    a) girls and boys alternate

    My logic is:
    arrange boys first, there are 4! ways of arrangement
    There are then 5P4 ways of arranging girls, consider one may be before a boy or after a boy

    So this is not the right answer. But where is the flaw in my logic. Where did i over count?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,394
    Thanks
    1478
    Awards
    1
    Quote Originally Posted by Lukybear View Post
    How many ways can 4 different boys and 4 different girls be arranged in a line if a) girls and boys alternate.
    In your count the girls and boys may not alternate.
    Answer: 2\cdot(4!)^2. WHY?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jul 2009
    Posts
    132
    Understood thanks.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Probability of boys and girls
    Posted in the Statistics Forum
    Replies: 10
    Last Post: January 8th 2011, 08:16 AM
  2. 8 boys and 10 girls in the class
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: November 29th 2010, 05:43 PM
  3. boys and girls in a family
    Posted in the Statistics Forum
    Replies: 1
    Last Post: November 12th 2009, 09:38 PM
  4. Boys and Girls
    Posted in the Statistics Forum
    Replies: 5
    Last Post: November 4th 2009, 11:30 AM
  5. 5 boys and 4 girls in a line,no two girls together
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: June 5th 2009, 03:21 PM

Search Tags


/mathhelpforum @mathhelpforum