Evaluating the average occupancy of each energy state is much simpler than in the MaxwellBoltzmann example since each macrostate has a weight of 1. The average occupancy is just the sum of the numbers of particles in a given energy state over all the 5 distributions divided by 5.

Index Reference Blatt Ch. 11  

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The average distribution of 9 units of energy among 6 identical particles
For fermions, there are only 5 possible distributions of 9 units of energy among 6 particles compared to 26 possible distributions for classical particles. To get a distribution function of the number of particles as a function of energy, the average population of each energy state must be taken. The average for each of the 9 states is shown above compared to the results obtained by MaxwellBoltzmann statistics and BoseEinstein statistics . Low energy states are less probable with FermiDirac statistics than with the MaxwellBoltzmann statistics while midrange energies are more probable. While that difference is not dramatic in this example for a small number of particles, it becomes very dramatic with large numbers and low temperatures. At absolute zero all of the possible energy states up to a level called the Fermi energy are occupied, and all the levels above the Fermi energy are vacant. 
Index Reference Blatt Ch. 11  

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