Chapter 4: Counting
We will now begin discussing counting. In counting, we answer the question how many?:
How many ways can we arrange the letters in MISSISSIPPI?
How many factors of 1200 are multiples are 24?
How many ways can we select 4 boys and 3 girls from a group of 10 boys and 5 girls?
This chapter will be relatively example heavy. We will start by establishing some of the more basic counting rules, before generalizing some common patterns to the ideas of permutations and combinations. In the latter half of the chapter, we will discuss Pascal’s triangle, and the idea of a combinatorial proof. In Chapter 5, to round out the course, we will extend these ideas to polynomials; specifically, the Binomial Theorem is an application of combinatorial techiques that has many interesting applications.