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Permutation and Combination

  1. Sep 20, 2008 #1
    1. The problem statement, all variables and given/known data

    Find the number of arrangements possible for arranging m+n things in a circular orientation, such that m things are alike and th other n things are also alike but of diffrent kind as from the first category.

    Attempt:
    I fix one thing. I am left with m+n-1
    So the number of arrangements should be= [tex]\frac{(m+n-1)!}{(m-1)!n!}[/tex]
    what is wrong with this approach???
     
  2. jcsd
  3. Sep 20, 2008 #2

    tiny-tim

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    Hi ritwik06! :smile:

    Hint: if m = n = 2, there are only two possible arrangements … AABB and ABAB, but your formula gives 3!/2! = 3, because it includes ABBA.

    Can you see why that's wrong, and how to deal with it? :wink:
     
  4. Sep 21, 2008 #3
    Yeah, Thats wrong.
    So what should I do know? How can I check?? Is it only one arrangement that repeats itself?? Or Are there more? How can I find out? Making possible cases is easy when m,n are small but hen they are big its difficult. Help me please.
     
  5. Sep 21, 2008 #4

    tiny-tim

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    Come on … think! :smile:

    ABBA is wrong because … ? :wink:
     
  6. Sep 21, 2008 #5
    Its wrong because its the same as AABB....
    But still, I want to generalise the result not by fixing m or n :eek:
     
    Last edited: Sep 21, 2008
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