Hello! In order to obtain the number of actual electrons in the conduction band or in a range of energies, two functions are needed: 1) the density of states for electrons in conduction band, that is the function [itex]g_c(E)[/itex]; 2) the Fermi probability distribution [itex]f(E)[/itex] for the material at its temperature [itex]T[/itex]. (as a reference, this link can be used). So, the number of electrons between the energy level [itex]E[/itex] and the energy level [itex]E + dE[/itex] is given by [itex]n(E)dE = g_c(E) f(E) dE[/itex] where [itex]g_c(E) dE[/itex] is the number of states between energy level [itex]E[/itex] and energy level [itex]E + dE[/itex] and [itex]f(E)[/itex] is the probability that they are occupied. This would work if the number of states in that range is just 1 or 0. But what if there are multiple available states? Fermi probability distribution gives the probability that a state at a certain energy [itex]E[/itex] is occupied: it is just one state. If we need to handle multiple states (like two electrons with opposite spin) at the same energy (or in the same infinitesimal interval of energies, between [itex]E[/itex] and [itex]E + dE[/itex]), how should we use the value of the Fermi probability for each of them?