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# Start here!

Overview of this topic

# 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

Below are the relevant Common Core State Standards for both lessons in this topic:

## Lesson 1: Building crowds

Appropriate for all ages and introduces the counting principle (Grade 4-7 appropriate).

• CCSS.7.SP.C.8.B
• Relevant because we explain compound events using tree diagrams (counting principle).

## Lesson 2: Counting Crowds

This lesson begins with permutations and reaches the high school level. (Grade 7+ appropriate)

#### High School

• HSS-CP.B.9
• Relevant because we are using combinations to solve problems involving compound events.
• HSA-APR.C.5
• Relevant because binomial coefficients are terms in the binomial theorem expansion.