# 3. TreeÂ challenge

## Video transcript

- Great work, but suppose the director decides that we need robots made up of a little more variety and now, we need three kinds of parts; heads, bodies, and arms. When there are three parts to combine, the table doesn't work anymore. We need some other way to think about all the different ways that three parts can be combined. It would be even better if we can think of a way that works for two, or three, or four, or even more kinds of parts. When I first start trying to solve a new problem, I like to break that problem down into a bunch of smaller parts that are easier to solve. In this case, counting the number of robots made from two heads and three bodies. I can illustrate the two ways of selecting a head using a picture like this. And, I can illustrate the three ways of selecting a body using a picture like this. The problem with these picture so far is, they make it look like there are only five possible combinations. Before moving on to the next video, see if you can combine these two diagrams to show that there are six different combinations of robots.