A system consists of two independent particles. There are three available energy levels, i.e., 0, ε, and 2ε, for each particle. (a) Give the partition function if the particles obey (i) classic statistics, and the particles are distinguishable; (ii) classic statistics and the particles are indistinguishable; (b) Enumerate all the possible configurations if the particles obey (i) Fermi-Dirac statistic and (ii) Bose-Einstein statistics, and provide the corresponding partition functions.