I have this question on my homework that has been bugging me for a couple of days now and I was wondering if anybody could help me out. Let me set the scene.

We have N particles in total in a box of volume V. We split the box into V1 and V2 with a probability of p for a particle being in V1 and a probability of 1-p for the particle being in V2.

I need to find the average particle number in V1, i.e. <N1> and it's fluctuation dN1 for bot distinguishable and indistinguishable particles.

I hope somebody can help me. Thanks