  In this paper, the fourth in the series, we continue our study of
combinatorics in chaotic Newtonian dynamics. We focus once again on the chaotic
four-body problem in Newtonian gravity assuming finite-sized particles, and
interactions that produce direct collisions between any two particles. Our
long-term goal is to predict the probability of a given collision event
occurring over the course of an interaction, as a function of the numbers and
properties of the particles. In previous papers, we varied the number of
interacting particles, as well as the distributions of particle radii and
masses. Here, we refine the methods developed in these preceding studies, and
arrive at a final and robust methodology that can be used to study collisional
dynamics in a variety of astrophysical contexts, ranging from stars in star
clusters, galaxies in galaxy groups and clusters and even the collisional
growth of planetesimals in protoplanetary disks. We further present and refine
the concept of a Collision Rate Diagram (CRD), the primary tool we use to
quantify the relative rates for different collision scenarios to occur. The
agreement between our final theoretical model and the results of numerical
scattering simulations is excellent.

Solar and Stellar Astrophysics;Classical Physics