The Popularizing And Application Of Stirling Numbers In Classical Probability

Combinatorics to study the structure of a combination of the finite set of counting problems in the given conditions. Binomial coefficient, Stirling numbers, Polynomial coefficients, Bernoulli numbers, Euler numbers, Bell numbers, Catalan number and the Fibonacci numbers are the count of the classic combinatorial mathematics count.Probability theory and combinatorial mathematics are closely related, the combination of mathematical knowledge is applied to the problem of probability to important significance. Stirling number of new ideas for solving probability problems, especially in certain discrete random variables, the Stirling number of the introduction of an effective and special methods. Combinatorics and probability combination of knowledge, is the mathematical theory of a new and important ideas. Scholars have come to the study of the Stirling numbers of the large number of conclusions, the paper first describes the two types of Stirling numbers and their promotion in the form count tool, then focuses on these counting problems in the classical probability calculations.Researching this subject, what made us get further study and master to Stirling numbers. Deeply research Stirling numbers'role and value in the application of classical probability. At the same time, explored or proved new conclusion on combinations as possible as we can. Proved the probability of combinatorial identities so that add the contents of Stirling numbers.