Colloidal clusters consist of small numbers of colloidal particles bound by weak short-range attractions. The equilibrium probability of observing a cluster in a particular geometry is well described by a statistical mechanical model originally developed for molecules. To explain why this model fits experimental data so well, we derive the partition function classically, with no quantum-mechanical considerations. Then, by comparing and contrasting the derivation in particle coordinates with that in center-of-mass coordinates, we physically interpret the terms in the center-of-mass formulation, which is equivalent to the high-temperature partition function for molecules. We discuss, from a purely classical perspective, how and why cluster characteristics such as the symmetry number, moments of inertia, and vibrational frequencies affect the equilibrium probabilities.