Dear Chegg, I need help with following question, and hope that someone can help

Question

Dear Chegg, I need help with following question, and hope that someone can help me;

Non-Interacting Adsorbates (Langmuir Isotherms) Figure 1: Surface in contact with a gas of particles A. Top view showing the structure of N particles adsorbed on the M atom large surface, Side view illustrating the exchange of particles between the surface and the gas. Start by considering a surface consisting of M surface atoms placed on a square lattice (see figure 1), on which N non-interacting particles A have been adsorbed. Assuming that each surface atom can bind either zero or one particle, write down an expression for the multiplicity W(M>N), i.e. the number of possible distinguishable arrangements of N particles on the M surface atoms. Use that the M lattice sites are distinguishable, while the N adsorbed particles are indistinguishable.

Explanation / Answer

Total possilbe sites = M

So arrangements possible for one particle = M!

Number of particles = N

arrangements possible = (N + 1 )!

so possible distinghuishable arrangements = M ! / (N + 1)!

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