Counting and Combinatorial Analysis
Gérard-Michel Cochard, Mhand Hifi · 2025
Counting problems are extremely difficult to solve manually. Computers have proven highly effective in tackling these fundamental problems, which quickly surpass human calculation capabilities. The ability to identify and count object pairings falls within the domain of combinatorial analysis. This chapter covers the counting of permutations, arrangements and combinations. The chapter details the properties of binomial coefficients. The name of the binomial coefficient comes from Newton's binomial, a formula given by Isaac Newton which is a remarkable identity. The counting problem involves finding the number of elements in a finite set. The number is called the cardinal of the set. The chapter describes the use of Stirling's formula for combinatorial calculation.