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Multiplicity of a two state system

  1. Oct 3, 2013 #1

    d2x

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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:

    [itex]Ω=2^N[/itex],

    but what about the definition:

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

    Clearly:
    [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?
    Thanks.
     
  2. jcsd
  3. Oct 3, 2013 #2
    If you sum the second one over n you get the first one.
     
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