Comparison of the thermodynamic entropy with Boltzmann's principle shows that under conditions of constant volume the total number of arrangements in a simple thermodynamic system with temperature-independent constant-volume heat capacity, C, is T[superscript C/k]. A physical interpretation of this function is given for three such systems: an ideal monatomic gas, an ideal gas of diatomic molecules with rotational motion and a solid in the Dulong-Petit limit of high temperature. T[superscript 1/2] emerges as a natural measure of the number of accessible states for a single particle in one dimension. Extension to N particles in three dimensions leads to T[superscript C/k] as the total number of possible arrangements or microstates. The different microstates of the system are thus shown "a posteriori" to be equally probable, with probability T[superscript -C/k], which implies that for the purposes of counting states the particles are distinguishable. The most probable energy state of the system is determined by the degeneracy of the microstates. (Contains 1 figure.)