Entropy of an ideal gas using statistical thermodynamics

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I cam across a question that asks for the entropy of an ideal gas of N molecules in which the energy of each molecule can assume 2 and only 2 distinct values 0 and E. It gives occupation numbers to represent the energy levels respectively with a fixed total energy.
Now I know S=kln(omega) = ln{N!/(n0!n1!)}. Am I to understand that this system is distinguishable and I ould use Bolzmann statistics or would I just go through the rigormorale of the stirling approximation. Guidance would be appreciated.
 

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