Figure 1: Bose-Einstein and Fermi-Dirac Counting
give the number of Bose-Einstein, Fermi-Dirac, and Boltzmann complections depicted, which would contribute to the overall counting problem in statistical thermodynamics.
One has for the number of (distinguishable) Boltzmann states
but the number of indistinguishable states is
which is the Boltzmann value corrected for indistinguishability. The number of Bose-Einstein states is
and the number of Fermi-Dirac states is