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Thread: Question dealing with combinations

  1. #1
    Junior Member
    Sep 2009

    Question dealing with combinations

    Imagine n molecules of gas confined to a rigid container divided into two chambers by a semipermeable membrane. If i molecules are in the left chamber the entropy of the system is defined by the equation

    Entropy = log (n choose i)

    If n is even, for what configuration of molecules will the the entropy be maximized?

    (As a hint it says: Consider proving that successive terms in the sequence (n choose 0), (n choose 1), ..., (n choose n) first increase and then decrease).
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  2. #2
    MHF Contributor
    Apr 2008
    What you really want to show is that $\displaystyle n \choose {n/2}$ maximizes $\displaystyle n \choose i$.
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