Problem- Consider a generalized energy level system of energy levels, numbered 0 (the ground state), 1 , 2 , 3 ... i ...., with respective energies ?0, ?1, ?2, ?3 ... ?i ...., and respective populations n0, n1, n2, n3 ... ni ....

Derive the Boltzmann equation by:

(i) Promoting one particle from the ground state to the i th level by inputting an energy ?i,

(ii) Calculating the change on the number of ways W of arranging the system, where W = N! / (n0! n1! n2! n3! ... ni !....)

(iii) Calculating the change in entropy using the Boltzmann equation

S = k lnW

I am not able to determine the correct answer for the above question please helps me to get the correct answer