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Help with permutations and combinations

  1. Jan 17, 2005 #1
    How do u calculate the the total number of combinations, given that you have n number of object and you will choose r of the objects, but x of these objects are mutually exclusive. Let x=2 for your explanations.

    I kinda have an idea on how to do this, but i cant frecall an formula for the calculations.

    Total number of permutations would be [tex]\frac{n!}{(n-r)!r!}[/tex] And now i have to subtract from this, the number of combinations with one of the mutually exclusive events given that the other has happened.

    P.S. Maybe i should post a question to help you understand better ? ..., as my linguistic skills are not top-notch.
     
    Last edited: Jan 17, 2005
  2. jcsd
  3. Jan 18, 2005 #2
    If the objects are mutually exclusive that means you can only select 1 of them. So you choose from n - x + 1 objects, and multiply it by x ways to choose from the x objects.
     
  4. Jan 20, 2005 #3
    I don't think that's quite right. It ignores the combinations that don't have one of the x objects.
     
  5. Jan 20, 2005 #4
    A solution for this problem is:

    [tex]\binom{n}{k}-\sum_{i=2}^{x}\left[\binom{x}{i}\times\binom{n-x}{k-i}\right][/tex]

    I'm sure there's a more elegant formulation, but this one works.

    Of course, for x=2, this simplifies to:

    [tex]\binom{n}{k}-\binom{n-2}{k-2}[/tex]
     
    Last edited: Jan 21, 2005
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