Canonical lattice-gas partition function ($Z_N=\left(\genfrac{}{}{0ex}{}{M}{N}\right)e^{-\beta N{\epsilon }_s}$)

For $N$ indistinguishable adsorbates on $M$ equivalent sites, at most one per site and no lateral interactions, $Z_N=\left(\genfrac{}{}{0ex}{}{M}{N}\right)e^{-N{\epsilon }_s/(k_{B}T)}$. The binomial coefficient already accounts for indistinguishability; an additional division by $N!$ would count it twice.