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[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.