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A Problem in Discrete Probability

  1. Oct 3, 2008 #1
    I recently came across a page named "Gems of Discrete Probability" - http://www.cse.iitd.ernet.in/~sbaswana/Puzzles/Probability/exercises.html

    Being a mathematics enthusiast, I tried the first question. Being very rusty in probability, I failed to come up with a satisfying answer: the best I got (for the first question, the expected number of empty bins) was an "open" formula:

    n /n\ /n-1\
    ∑ k * \k/ * \ k /
    k=0
    ----------------------
    /2n-1\
    \ n /
    /n\
    Where the notation \k/ is the binomial coefficient, n!/k!(n-k)! .
    Is there any way to get rid of the ∑ here, is my solution wrong, is there any way to solve it that will not result in a sum, or is that the best answer?
    Thanks in advance,
    Woolly Rhino.
     
    Last edited: Oct 3, 2008
  2. jcsd
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