Geometrical Approach to the Theory of Probability

The purpose of this paper is twofold: first, we wish to present an interesting geometrical approach to the derivation of some familiar equations in the theory of probability, and second, we wish to use this newer approach for extending the scope of the equations. Particularly, we wish to extend the well-known problem of how many ways there are of distributing m identical objects among n numbered boxes with no more than one in each box to the problem of distributing the m objects in n boxes with no more than M in each box. The solution of this more general problem of M as the limiting number per box is expressed as a mathematical series involving factorials.