Results 1 to 2 of 2

Math Help - Another Permutation question

  1. #1
    Newbie
    Joined
    Sep 2011
    Posts
    5

    Question Another Permutation question

    Here is my question
    In how many ways can 8 library books be arranged on a shelf if 3 of the books cannot be all together?

    What i did is:
    3 books cannot be together meaning there can be two, one or even none of the three 'special' books are in the arrangements.

    If there are two 'special' books:
    7 books available for arrangement: 7P7 = 5040
    And because 2 out of 3 books are available so there will be 6 possible arrangements for the 'special' books. Therefore, 7P7 x 6 = 30240

    If there are one 'special' book:
    6 books are available for arrangement: 6P6 = 720
    1 out of 3 'special' books are available so 3 possible arrangement for the 'special' books. Therefore, 6P6 x 3 = 2160

    If there no 'special' book:
    5 books are available for arrangement: 5P5= 120

    Adding them all together should get 30240 + 2160 + 120 = 32520 arrangements

    But the answer is 36000

    What did i do wrong?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,649
    Thanks
    1597
    Awards
    1

    Re: Another Permutation question

    Quote Originally Posted by richardyuen2144 View Post
    Here is my question
    In how many ways can 8 library books be arranged on a shelf if 3 of the books cannot be all together?
    There are five books that are separators.
    __X__X__X__X__X__ which create six places to place the three special books.

    BTW this is were all three are separated from one another.
    Last edited by Plato; September 2nd 2011 at 06:29 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Another Permutation question
    Posted in the Statistics Forum
    Replies: 2
    Last Post: December 6th 2010, 06:12 PM
  2. permutation question
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: November 19th 2009, 08:47 PM
  3. Permutation question.
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: June 16th 2009, 05:09 AM
  4. permutation question
    Posted in the Statistics Forum
    Replies: 4
    Last Post: June 1st 2009, 04:16 PM
  5. Permutation Question
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: March 30th 2009, 12:13 PM

Search Tags


/mathhelpforum @mathhelpforum