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### Course: Pixar in a Box > Unit 5

Lesson 2: Counting crowds- Start here!
- 1. Two headed robots
- Counting two-headed robots
- 2. Snake bots
- Construção de robôs em formato de cobra
- 3. Calculating factorials
- Calculating factorials
- 4. Casting problem
- Counting casts 1
- 5. Does order matter?
- Counting casts 2
- 6. Binomial coefficient
- Combinations

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# Start here!

# Ready to dive into some more math?

In the first lesson you learned that it was possible to build 1000

*possible*robots using only a handful of parts. Now suppose the director only asks for a cast of 6*different*robots from the set of 1000 possible robots. How many possible casts would this result in?This question is easy IF you know how to think about it. In this lesson we are going to develop a really powerful formula we can use to answer questions like this. It's known as the

**binomial coefficient**:Specifically we'll want to answer this question: given $n$ possible robots how many different casts could we make of size $k$ ?

To get there we are first going to introduce

**permutations**by counting the number of*different*robotic snakes we can build by rearranging the*same set*of parts.Finally we'll combine the ideas of permutations and combinations to arrive at the general form of the binomial coefficient:

# What do I need to know before starting?

- You should have finished the first lesson
- You should be comfortable with algebra basics
- Remember, you can always work through part of the material