Three distinguishable particles (meaning they can be labeled A,B,C) are to be distributed among five energy levels with energies 0,? , 2?, 3?, and 4?. There is only one state at each energy level (no degeneracy). Assume the total energy of this system is U = 4?. A macrostate of this system is specified by the number of particles in each energy level; we can label each macrostate with five numbers, the number of particles in each level: (N0, N1, N2, N3, N4).

(a) Determine the total number of possible macrostates.

(b) For each macrostate, determine the number of microstates ω.

(c) Which macrostate(s) is/are most probable, and what the probability that it/they will occur?

(d) Suppose 1 particle with zero energy is added to the system. How do the results of parts (a-c) change?

(e) Try to generalize your result. If the number of particles N is very large (but the energy of the system stays fixed at U = 4?), which macrostate becomes overwhelmingly likely?