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## 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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# 5. Casting challenge

Now it's your turn to drive. In this video we'll present you with a casting challenge to complete using everything we've learned so far.

## Want to join the conversation?

- wait are we doing math?(2 votes)
- i has question ):B can you do dis math in like well how long does it take you tah do dis math? cause is like... it takes waaaay to long for me to do it... ):B(0 votes)
- You should memorize your multiplication facts so that it only takes a second or two to know the answer to problems like this. In the meantime, try using a calculator.(4 votes)

## Video transcript

- The advantage of this diagram,
is that since it represents all of the choices you
have, we can just add more and more choices to the bottom. So, if we have two heads and
three bodies and three arms, then the diagram would look like this, for a total of two
times three times three, or 18 different combinations. These are sometimes called
tree diagrams, because when you turn them over,
they look a lot like a tree. The diagram has helped us
understand that we just need to multiple the number
of each kind of part. So, if we're just interested
in how many combinations are needed, we don't
need the diagram anymore. And, the number of
combinations gets big fast. For instance, if we had
five heads, six bodies, and seven arms, and say, eight
different kinds of wheels on our robots, we would
have to build five plus six plus seven plus eight, or 26
different kinds of objects. But, we could build five times
six times seven times eight, or 1,680 different robots. Because there are so many
possible combinations, it's easy to go crazy and
build a huge crowd of robots. (robots flying through the air
and rolling across the floor) (crashing and squeaking) - Emmet! - While a big crowd of robots might make the film more exciting,
we have to keep in mind that the more robots there are, the more robots the
animators have to animate and the more robots the
computer needs to deal with. So, we're always trying
to achieve our artisticals in the most efficient way possible. Now, it's time to put you to work. Your job with this interactive,
is to make both the director and the producer happy. You should have a wide variety of robots, so that there's a lot of visual interest and the director is happy with your work. But, you should keep the cost down, so that the producer is
happy with your work. The cost of each part is shown,
select a subset of heads, bodies, and arms so that combining
them in all possible ways gives exactly 12 robots and
the cost of all the parts must be below $300. The director and producer
will be here in 10 minutes to review your work. I know you got this.