Results 1 to 14 of 14

Math Help - Seating arrangements.

  1. #1
    Newbie
    Joined
    Mar 2011
    Posts
    7

    Seating arrangements.

    quite confused with this particular question...

    How many ways can 9 students(5 girls and 4 boys) be seated in a row if

    there are no restrictions and if the first 3 must be boys?

    i think its the difference in number of boys and girls that is confusing me
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member Sambit's Avatar
    Joined
    Oct 2010
    Posts
    355
    When there is no restriction, the possible number of ways is simply 9!.
    When the first 3 must be boys, these 3 boys can sit in 3! ways and the rest 6 can sit in 6! ways. Hence the total number of possible ways in this case is 3!*6!.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2011
    Posts
    7
    ok i used what you showed and got farther into the question, but am not stuck at alternating seating girl then boy AND boy then girl?
    would it be 5!*4!*9!? does it change if going from girl > boy instead of boy >girl?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,860
    Thanks
    741
    Hello, slowlearner!

    How many ways can 5 girls and 4 boys be seated in a row
    if the first 3 must be boys?

    Select three of the four boys: . {4\choose3} \,=\,4 choices.
    Seat them in the first three chairs: . 3! \,=\,6 ways.
    Seat the other six children: . 6! = 720 ways.

    Therefore, there are: . 4\cdot 6\cdot 720 \:=\:17,\!280 ways.

    Last edited by Soroban; March 11th 2011 at 05:39 AM. Reason: Corrected silly error . . . *blush*
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Mar 2011
    Posts
    7
    How would i find out how many ways the 5 girls and 4 boys could be seated if the seating must alternate girl then boy? im quite confused here, is it 5!4!(9*8*7*6*5)? that is just my shot in the dark, im not quite sure how to solve this scenario
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,906
    Thanks
    1757
    Awards
    1
    Quote Originally Posted by slowlearner View Post
    How would i find out how many ways the 5 girls and 4 boys could be seated if the seating must alternate girl then boy? im quite confused here, is it 5!4!(9*8*7*6*5)? that is just my shot in the dark, im not quite sure how to solve this scenario
    Note that the way you have written the question the row must begin with a girl.
    So the answer is (5!)(4!).
    Sit a girl in ever other seat, then put a boy between them.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Mar 2011
    Posts
    7
    thank you! so if you were to seat it boy then girl then it would just be (4!)(5!)? or can this not be done since it would end up being girl next to girl at the end due to only 4 boys?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,906
    Thanks
    1757
    Awards
    1
    Quote Originally Posted by slowlearner View Post
    thank you! so if you were to seat it boy then girl then it would just be (4!)(5!)? or can this not be done since it would end up being girl next to girl at the end due to only 4 boys?
    But then you have two girls sitting together at the last two seats. Do you allow that?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Mar 2011
    Posts
    7
    thats what i was asking myself :P its got me quite confused. probability and statistics have been killing me all semester!
    Follow Math Help Forum on Facebook and Google+

  10. #10
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,906
    Thanks
    1757
    Awards
    1
    Quote Originally Posted by slowlearner View Post
    thats what i was asking myself :P its got me quite confused. probability and statistics have been killing me all semester!
    It is not "probability and statistics have been killing" you but the meaning of the language. It says that the girls and boys must alternate.
    So it got be gbgbgbgbg.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Newbie
    Joined
    Mar 2011
    Posts
    7
    i agree! i think it could possibly be 6! * 4! * 3 * 2 * 1?
    Follow Math Help Forum on Facebook and Google+

  12. #12
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,906
    Thanks
    1757
    Awards
    1
    Quote Originally Posted by slowlearner View Post
    i agree! i think it could possibly be 6! * 4! * 3 * 2 * 1?
    That is wrong.
    Follow Math Help Forum on Facebook and Google+

  13. #13
    Newbie
    Joined
    Mar 2011
    Posts
    7
    Quote Originally Posted by Plato View Post
    That is wrong.
    can you elaborate?
    Follow Math Help Forum on Facebook and Google+

  14. #14
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,906
    Thanks
    1757
    Awards
    1
    Quote Originally Posted by slowlearner View Post
    can you elaborate?
    See reply #6. That is the answer. PERIOD!
    Over and out.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Seating arrangement
    Posted in the Statistics Forum
    Replies: 5
    Last Post: September 30th 2010, 10:49 AM
  2. Seating plans
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: September 4th 2010, 11:09 PM
  3. Seating arrangements problem
    Posted in the Statistics Forum
    Replies: 0
    Last Post: November 8th 2009, 05:08 PM
  4. Seating arrangements
    Posted in the Statistics Forum
    Replies: 4
    Last Post: February 19th 2009, 03:03 PM
  5. seating problem
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: November 20th 2007, 06:17 PM

Search Tags


/mathhelpforum @mathhelpforum