Ensembles of particles obeying Fermi-Dirac statistics are considered from a point of view which is analogous to some recent work of Mayer on classical particle statistics. The density functions ${\rho }_n$ are defined for $n$ much smaller than the average number of particles in the ensemble. Since the knowledge of only a few ${\rho }_n$ is sufficient for the computation of most averages of physical interest, it is important to compare different ensembles with the same density functions, say ${\rho }_1$ and ${\rho }_2$. The ensemble with the largest entropy is constructed as being the most significant. A number of simple examples are briefly considered.

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