In the first meeting of Fall 2018, we introduced the theme for the semester: Combinatorics. This is a fancy word in mathematics that encompasses counting problems, enumerations, as well as structure and design problems.
For this lesson, we focused on four kinds of counting problems. All four problems involved a kind of sampling, but with different rules each time. We tried sampling with and without replacement, and also with order mattering and not mattering.
Each problem also led to its own mathematical analysis, and ultimately to a set of four handy formulas which can be reused in many different situations!