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## Pixar in a Box

### Course: Pixar in a Box > Unit 13

Lesson 1: Building crowds- Start here!
- Introduction to combinatorics
- 1. Counting with tables
- Table of combinations
- 2. Robot combinations
- Robot combinations
- 3. Tree challenge
- 4. Counting with trees
- Tree of combinations
- 5. Casting challenge
- Casting challenge
- Getting to know Fran Kalal
- Hands-on activity

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# 3. Tree challenge

How can trees be combined to count robots with many parts?

## Want to join the conversation?

- cant you just make the table in three diamensions(10 votes)
- Theoretically you can, but it's difficult to create and read 3D tables.(10 votes)

- Why can't we make them 3 dimensonal?(3 votes)
- i am in your walls(3 votes)
- Ya know, I think this is an older video. Like, from 2017 or something. Not recent.(1 vote)
- I don't know, yet.(1 vote)
- It aint possable at all(1 vote)

## 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.