Problem: Consider a non-interacting system of 4 particles with each particle having single-particle states with energies equal to 0, e, 2e and 3e. Given that the total energy of the system is 6e, find the number of microstates of the system (and identify the microstates) if the particles are a) distinguishable, b) indistinguishable Bosons and c) indistinguisable Fermions. For a) I get 3-ways to get 6e and 3*4 ways to get 6e amoung distinguishable particles. For b) I get 3-ways to get 6e amoung the indistinguishable Bosons. For c) I get 1-way to get 6e amoung Fermions. Is this correct? Also is there such thing as distinguishable Fermions. My guess is by definition of a Fermion, no! Thanks.