Primary reference: Chapter 3 (Counting) of Book of Proof by Richard Hammack

richardhammack.github.io

Content covered in this unit includes:

• The concept of a list, i.e. an ordered sequence of objects

• The multiplication principle for counting lists, with or without repetition

• The definition of a permutation or a $k$-permutation of a set

• The factorial of a natural number, and the use of factorials to count ($k$-)permutations of sets

• The definition of the binomial coefficient

  $$ \begin{pmatrix} n \\ k \end{pmatrix} $$

  and the use of binomial coefficients to count subsets of a given set