my attempt to the question is as follow :

W is the arrangement factor where N is the total number of states while n is the are the number of particles in energy state, Ei.

the relationship between between the entropy and the arrangement factor is

S=k ln W...

I really didn't understand the last part of the question... however, this is my attempt :

Since all the states are equiprobable to occur, the probability of the 1st level is 1/6 x 5 = 5/6 and the probability of the 5th level is 1/6 x 1 = 1/6 while the arrangement factor, W for the 1st level is (6 x 5 x 4 x 3 x 2)/5! = 6 and the arrangement factor, W for the 5th level is = 6!/1! = 720.... is that means the probability for 1st level is 6/726 and the probability for the 5th level is 720/726????? i get confuse with the earlier probability and the arrangement factor??? what it has to be related with entropy???? anyone can clarify it????

and the arrangement factor = probabalility iff all the molecules are at T = 0 which means S = 0.... based on the example. probability = 1/6 x 6 = 1 and the arrangement factor, W = 6!/6! = 1...

is my understanding towards the question is correct or I just misunderstanding it???

ANYONE CAN CLARIFY IT??? PLZ3X