· The Thermodynamic probability, W, is given in terms of N and n:

W = {N!/n!(N - n)!}

· The configurational entropy of the n vacancies is then given by:

S_n= k Ln{N!/n!(N - n)!}

· The Gibbs function of the n-vacancy system then becomes:

G_n = G₀ + nH_v - kT Ln{N!/n!(N - n)!}

substituting for the configurational entropy, S_n, gives us :