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The density of states functions in quantum mechanical distributions give
 

a. the number of particles at a given energy level.
  b. the number of energy states available per unit of energy range.
  c. the statistical factors for the Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein distributions.
  d. the energy at which the density of particles occupying that state is the greatest.

b.
The density of states functions are vital to quantum mechanical distributions because they give the number of energy states per unit of energy range. Without this number, the functions to find the numbers of particles at a given energy level range would be useless.

Appreciate your effort, thank you