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# Multiplicity function for N noninteracting spins

The multiplicity function for a two state paramagnet, Ω(n,N), is the number of spin states such that n of the N spins point in the z-direction. This function is given by the combinatoric function C(N,n). That is:

$\Omega (n,N) = {N \choose n} = {{N!} \over {n!(N - n)!}}$
$S = k\ln \Omega (n,N) \,$ [1] Where k is the Boltzmann constant