Application Of The Probability Method In Proving Combinatorial Counts

Combinatorial identities proof method is varied, the probability method is a relatively new one. In this paper, the probability method and the binomial theorem method is used to study series of combinatorial identities as the second kind Stirling Numbers, harmonic number, Bell number, derangements, and generalized Hermite polynomial,etc. and draw some new identity between them simultaneously. The main work is as follows:Chapter 2:we studied some identities of the second kind Stirling numbers, harmonic number, Bell number, derangements. Firstly, the probability expression of the classi-cal combinatorial sequences is given. Secondly, proved the above identities between the classical combinatorial sequences, by using the properties of expectations and binomial theorem, and obtained some new identities among harmonic number, Bell number and derangements.Chapter 3:some identities between Hermite polynomial and generalized Hermite polynomial is discussed. First of all, the relationship between them and the corresponding probability is given. Then, obtained some identities between them by the appropriate application of normal distribution properties and the binomial theorem.