It is a typical introductory problem in classical statistical physics to calculate the entropy of a two-level-system: say we have a N particle system in which particles can have energy E or 0. Assuming the particles are distinguishable we simply calculate the number of microstates using the microcanonical ensemble and relate it with entropy.
My question is: what if the particles (of each energy level) are indistinguishable? The number of microstates is simply one, and therefore the entropy nule. I guess something is wrong in the reasoning but can't see what.
(of course we don't take into account if particles are bosons or fermions)