  In this article we propose a model based on the Statistical Bootstrap
approach to estimate the cross sections of different hadronic reactions up to a
few GeV in c.m.s energy. The method is based on the idea, when two particles
collide a so called fireball is formed, which after a short time period decays
statistically into a specific final state. To calculate the probabilities we
use a phase space description extended with quark combinatorial factors and the
possibility of more than one fireball formation. In a few simple cases the
probability of a specific final state can be calculated analytically, where we
show that the model is able to reproduce the ratios of the considered cross
sections. We also show that the model is able to describe proton\,-\,antiproton
annihilation at rest. In the latter case we used a numerical method to
calculate the more complicated final state probabilities. Additionally, we
examined the formation of strange and charmed mesons as well, where we used
existing data to fit the relevant model parameters.
