  We develop a formalism for calculating probabilities for the outcomes of
stellar dynamical interactions, based on results from $N$-body scattering
experiments. We focus here on encounters involving up to six particles and
calculate probabilities for direct stellar collisions; however our method is in
principle valid for larger particle numbers. Our method relies on the binomial
theorem, and is applicable to encounters involving any combination of particle
radii. We further demonstrate that our base model is valid to within a few
percent for any combination of particle masses, provided the minimum mass ratio
is within a factor of a few from unity. This method is particularly suitable
for models of collisional systems involving large numbers of stars, such as
globular clusters, old open clusters and galactic nuclei, where small subsets
of stars may regularly have very close encounters, and the direct integration
of all such encounters is computationally expensive. Variations of our method
may also be used to treat other encounter outcomes, such as ejections and
exchanges.
