Results 1 to 5 of 5

Math Help - Combination Question

  1. #1
    Newbie
    Joined
    Sep 2008
    Posts
    5

    Combination Question

    9 people drive into a parking lot, 4 are boys and 5 are girls. They decide to park in a straight row of 9, if none of the girls park next to each other, how many different parking arrangements are there?

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1
    Quote Originally Posted by RicLang View Post
    9 people drive into a parking lot, 4 are boys and 5 are girls. They decide to park in a straight row of 9, if none of the girls park next to each other, how many different parking arrangements are there?
    What if they are in only two cars?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2008
    Posts
    5
    Quote Originally Posted by Plato View Post
    What if they are in only two cars?
    They are each in one car.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,682
    Thanks
    614
    Hello, RicLang!

    9 people drive into a parking lot, 4 are boys and 5 are girls.
    They decide to park in a straight row of 9 spaces.
    If none of the girls park next to each other, how many different parking arrangements are there?

    If the girls are non-adjacent, there is ONE arrangement of the genders: . GBGBGBGBG

    Then the five girls can be arranged in: . 5! ways.
    The four boys can be arranged in: . 4! ways.

    Therefore, there are: . (5!)(4!) \:=\:(120)(24) \:=\:2880\text{ arrangements.}

    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Sep 2008
    Posts
    5
    Thanks alot!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Combination Question
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: September 16th 2011, 02:35 PM
  2. Combination question
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: August 28th 2011, 12:47 PM
  3. Combination question?
    Posted in the Statistics Forum
    Replies: 5
    Last Post: July 9th 2011, 01:17 PM
  4. Combination question
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: April 20th 2011, 09:04 AM
  5. Combination - KEY QUESTION
    Posted in the Statistics Forum
    Replies: 1
    Last Post: November 23rd 2008, 03:43 PM

Search Tags


/mathhelpforum @mathhelpforum