Ball-box Probabilistic Model And Combinatorial Identities

We use ball-box model to study the combinatorial identities. Aim is to find and certify combinatorial identities. We calculate these problems in different way. The main content is as follows in this paper:Ball-box model is said the mathematical models of n balls putted in m boxes .Although it is looked merely as a common combinatorial or a probabilistic problem ,but it contains many combinatorial tools. Such as generating function,integer partition,Stirling number etc. To choose this problem to discuss the different situations, we will get many interesting combinatorial conclusions. (Most is combinatorial identities). In fact it is including combinatorial explain of combinatorial identities. Because a new combinatorial explain of a equation have a high theory and actual application value .In this paper I'll use different ways to combine combinatorial math and probabilistic knowledge , so obtain different combinatorial identities. This is my new creation point.