Recall that a definition for the entropy is s = −∑ �% % ln �% where pi is the probability that the system is in state i and the sum is over all states which satisfy whatever constraints are placed on the system. note that this definition handles zero probability states and also produces an additive entropy when two non-interacting systems are combined. in all cases, suppose the volume of the system is fixed. the number of particles in each state is ni and the energy of each state is ei(a) suppose the number of particles in the system is fixed and the energy is fixed. what are the probabilities that maximize the entropy. of course, the sum will be include only those states which have the correct number of particles and energy. (or, equivalently, the probability for a state with the wrong number of particles or energy or both is 0.) in this and subsequent parts, you may have to introduce some auxiliary "constants." be sure to identify or give a physical interpretation for each such constant. hint: be sure to use the fact that the system is in some state: ∑% �%= 1.(b) now suppose the number of particles is fixed, but the system is in equilibrium with a heat bath such that its average energy is e. what are the probabilities that maximize the entropy? as before, be sure to identify or give a physical interpretation for any constants you introduce.(c) now suppose the system is in equilibrium with a heat bath and a "particle bath" (a reservoir with which it can exchange particles) such that the average energy is e and the average number of particles in the system is n . now what are the probabilities that maximize the entropy? as before, be sure to identify or give a physical interpretation for any constants you introduce.