Two energy level system calculate average occupancy

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1. Dec 14, 2016

Bananen

Hi!

I need help with the following question:
A system has two energy levels, ε and ε1 that can be occupied by fermions (spin=1/2) that are non-interacting from a reservoir at temperature T and chemical potential μ. Compute the avarage occupation number of the state with energy ε.

I have written down the grand canonical partition function and it is (1+e^(-β(ε-μ))^2)((1+e^(-β(ε1-μ)))^2)

and I know the formula for avarage occupation number for fermions is
ΣnP(n) where n goes from 0 to 1.

But then I'm stuck. The hint I got was that there can be up to four particles and there are different possibilities to put these into the energy levels.

Very thankful for any help!