Consider a system consisting of two particles, each of which can be in any one of three quantum states of respective energies 0, e and 3e. the system is in contact with a heat reservoir at temperature t=(kβ)^-1. since the number of particles is fixed, there is no need to consider the chemical potential.

a) write an expression for the partition function z if the particles obey classical maxwell boltzmann statistics and are considered distinguishable. you’ll need to enumerate all the states and sum over all of them.
b) what is z if the particles obey bose-einstein statistics?
c) what is z if the particles obey fermi-dirac statistics?