Today we’re going to learn a simple idea from a branch of math called combinatorics, which is all about clever ways to count things. The idea we’re learning is called the Product Rule.
The Product Rule says this: if you need to do two actions in a row, and the first action can be done in, say, \(5\) different ways, and for each of those choices the second action can be done in \(4\) different ways, then the total number of possible outcomes is \(5 \times 4\).
Why? Because every choice for the first action opens up all the possible choices for the second action. So each of the \(5\) first choices has \(4\) second choices that can follow it. Let’s see in a few examples this idea in practice: