Probability of Observing N particles in a given volume?

I'm having an issue with a probability problem concerning solutions.

Assume there is an "observational region" in a dilute solution with a volume V, and as solutes move across its boundary, the number N of solute molecules inside the observation region fluctuates.

Divide V into M regions of volume v each with n particles. The solution is dilute enough that $n=0$ or 1 (there is no v with more than one particle of solute), and each cell is occupied ($n=1$) with probability $p=({\rho}_{0})v$.

If W(N) is the number of configurations of the observation volume when N solutes are present, what is the probability P(N) of observing a given value of N, in terms of p,W(N),M, and N.

I know the probability $P({n}_{1},{n}_{2},\dots ,{n}_{M})$ of finding the system in a particular configuration in the observation volume is $p(N)={p}^{N}(1-p{)}^{M-N},$, (Bernoulli Distribution), and since there are N particles in M spaces then the maximum number of configurations is $\frac{M!}{(N!(M-N)!)}$

I'm not sure where to go from here.

I'm having an issue with a probability problem concerning solutions.

Assume there is an "observational region" in a dilute solution with a volume V, and as solutes move across its boundary, the number N of solute molecules inside the observation region fluctuates.

Divide V into M regions of volume v each with n particles. The solution is dilute enough that $n=0$ or 1 (there is no v with more than one particle of solute), and each cell is occupied ($n=1$) with probability $p=({\rho}_{0})v$.

If W(N) is the number of configurations of the observation volume when N solutes are present, what is the probability P(N) of observing a given value of N, in terms of p,W(N),M, and N.

I know the probability $P({n}_{1},{n}_{2},\dots ,{n}_{M})$ of finding the system in a particular configuration in the observation volume is $p(N)={p}^{N}(1-p{)}^{M-N},$, (Bernoulli Distribution), and since there are N particles in M spaces then the maximum number of configurations is $\frac{M!}{(N!(M-N)!)}$

I'm not sure where to go from here.