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A problem in permutation

  1. Mar 13, 2012 #1
    1. The problem statement, all variables and given/known data

    4 books by Shakespeare, 2 books are Dickens and 3 by Conrad are chosen for the problem. The question is to find the number of ways in which the books can be arranged s.t. the 3 Conrad books are separated.

    2. Relevant equations

    3. The attempt at a solution

    n(C separated) = n(w/o any restrictions) - n(3 C's together) - n(2 C's together).

    n(w/o any restrictions) = 9! because there are 9 items to be put in 9 places.

    n(3 C's together) = 3! * 7! because the 3 C's form a cluster: 3! for items within the cluster and 7! for all the items, considering the cluster as an item.

    n(2 C's together) = ... This is the tricky one as only 2 C's form a cluster and the number of places available for the other C depends on whether the cluster is at either of the edges of not.


    The answer is supposed to be 151,200 (from the back of the textbook), but I can't happen to get it.
     
  2. jcsd
  3. Mar 14, 2012 #2

    tiny-tim

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    hi failexam! :smile:
    good! :smile:

    but probably easier to start again, this way …

    the three conrad books have 4 "boxes" between and around them …

    how many ways to fit 6 items into 4 boxes, with only the outside boxes allowed to be empty?
     
  4. Mar 14, 2012 #3

    rcgldr

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    Note the middle 2 boxes have to have at least 1 book each, so that leaves the remaining 4 books to be placed in the 4 boxes in any pattern.
     
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