  In hot dense plasmas of intermediate or high-Z elements in the state of local
thermodynamic equilibrium, the number of electronic configurations contributing
to key macroscopic quantities such as the spectral opacity and equation of
state, can be enormous. In this work we present systematic methods for the
analysis of the number of relativistic electronic configurations in a plasma.
While the combinatoric number of configurations can be huge even for mid-Z
elements, the number of configurations which have non negligible population is
much lower and depends strongly and non-trivially on temperature and density.
We discuss two useful methods for the estimation of the number of populated
configurations: (i) using an exact calculation of the total combinatoric number
of configurations within superconfigurations in a converged
super-transition-array (STA) calculation, and (ii) by using an estimate for the
multidimensional width of the probability distribution for electronic
population over bound shells, which is binomial if electron exchange and
correlation effects are neglected. These methods are analyzed, and the
mechanism which leads to the huge number of populated configurations is
discussed in detail. Comprehensive average atom finite temperature density
functional theory (DFT) calculations are performed in a wide range of
temperature and density for several low, mid and high Z plasmas. The effects of
temperature and density on the number of populated configurations are discussed
and explained.
