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Homework Help: Multiplicity of a two state system

  1. Oct 3, 2013 #1


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    I only have a doubt about which definition to use for the multiplicity of a two state system. Clearly the total multiplicity of a two state system is given by:


    but what about the definition:

    [itex]Ω(N,n) = \binom{N}{n} = \frac{N!}{n!\cdot(N-n)!}[/itex].

    [itex]2^N ≠ \frac{N!}{2!\cdot(N-2)!}[/itex].

    What is the difference between these two expressions for multiplicity? Is the second one incorrect for a two state system of N things?
  2. jcsd
  3. Oct 3, 2013 #2
    If you sum the second one over n you get the first one.
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