Problem on the maxwell boltzmann expression

Question

Response to the following problem:

In the case of N distinguishable particles, the number of ways Ω, in which a macro state defined by N, particles in gl quantum states with energy ?_l, N₂ particles in g₂ quantum states with energy ?₂, ... , may be achieved, is given by the Maxwell Boltzmann expression

ΩBE = N!(g₁^N₁ g₂^N₂.../ N₁!N₂!...) ,

when gi » ni

(a) Using the Stirling approximation, calculate In Ω.

(b) Render In Ω a maximum, subject to the equations of constraint ∑N_i = N = const.and ∑N_i?_i = U = const, and explain why U and P should be the same as for indistinguishable particles, but S should be different.