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### 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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# 1. Counting with tables

How do we keep track of how many robots we've made?

## Want to join the conversation?

- 0:03what is the need of the bicycle(4 votes)
- 0:03the scooter is probably for quick transport throught the departments(3 votes)

- it wont let me watch this video... it says its "restricted" :((2 votes)
- Are you at school or an organization with a web filter?(1 vote)

- I all the sudden just want to watch brave.(3 votes)
- So if you were to design a humanoid type robot(2 arms and 2 legs along with a head and body) the number of robots you could make would be expressed by this formula:

(Arm)^2*(Leg)^2*Head*Body

where Arm, Leg, Head, and Body represent the number of different types of arms, legs, heads, and bodies right or am I missing something in those squared terms?(2 votes)- To find the combinations of the different body parts, you need to use the combination formula for each body part: n! / r!(n-r)! Use this formula for each of the body parts, and then multiply the answers of each formula to get the total combinations possible.(1 vote)

- hey can you do more videos about Fran Kalal I think she is a really good person to learn from and she is very happy and exited!(2 votes)
- I love your movie but how did you come up with the idea?(1 vote)
- Is there a lesson on adding animations or effects to a real video of move?(1 vote)
- I'm pretty sure that you use algebra to find how many robots you can make with a body and a head.(1 vote)
- where is the table thing(1 vote)
- what table thing are you talking about there are many tables?(1 vote)

- it's not letting me play the video(1 vote)
- they all work for me. go on youtube and make sure there isn't any restrictions on(1 vote)

## Video transcript

- Hi, I'm Fran Kalal. I'm a cloth and sim technical director at Pixar Animation Studios. That means I get to take what
I know about art and design and make outfits, and what I know about math and physics to make them move. I'm here today to talk to you about crowds like the large one behind me. Except that the one behind me is physical, and the ones we need to make for our films are virtual. That means they exist
only on the computer. We saw in the last video
how lots of robots were made using only a few parts through the use of combinatorics. So follow me to learn more about what combinatorics is and
how we use it at Pixar. To understand how many robots we can make from a bin of parts, let's
start with an example where a robot has one head and one body. And I've got two different
heads to choose from and three different bodies. So I can take this head with this body, or this same head with this body, and that's already two different robots. And clearly I can make a whole lot more. A great way to keep track
of this is with a table where I'm going to place
the heads along the columns and the bodies along the rows. This cell means put
this head on this body. There are six cells on the table, so there are six different robots even though we only have
five different parts. This is a great example of the fact that finding a good way
to think about a problem makes it easier to solve. How many robots could you make if there were different
numbers of heads and bodies? You can explore that question
in the next exercise.