# Combinatorics

We’ve recently talked about decision trees, game theory, and customer personas. For each topic, we’ve used examples that have a small number of cases so that we could show you something interesting, but manageable in size. Last week, we talked about how you can reduce the size of the problems you are trying to solve using clustering. This week, we will take one step even further back and talk about how to count the number of cases you have to start with.

To do this, we will talk about the mathematical field of combinatorics, in particular, permutations and combinations. A permutation counts the number outcomes where the order of what you are counting ** does** matter. A combination, on the other hand, counts the number of outcomes where the order of what you are counting

**matter. Both permutations and combinations are further broken down to consider whether the options of what you are choosing from is allowed to be repeated, i.e., replaced in the set of available options after each choice, or not (you’ll see this concept referred to as both “repetition” and “replacement” – I’ll use “replacement” this week). We will talk about each scenario this week:**

*does not*- Permutations with replacement
- Permutations without replacement
- Combinations without replacement
- Combinations with replacement

Let’s start counting!