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Probablity of fixed points in permutations

  1. Feb 14, 2008 #1
    Randomly permute (1,...,n). What is the probability that exactly i points are fixed?

    I think it should be


    Is it right?

    If so, is the expected number of fixed points (I know it's 1):


    But it doesn't sum to 1, I think
    Last edited: Feb 14, 2008
  2. jcsd
  3. Feb 14, 2008 #2


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    How is (n-i-1)! defined when i = n?
  4. Feb 14, 2008 #3
    It isn't. Nevermind. I was approaching the problem in a unnecessarily hard way.
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