This video [1:48] is an introduction to combinatorics. How to create a huge crowd of robots using only a few simple parts.

In the rest of this lesson, we're gonna look at a few other counting problems that come up when you try to make a large crowd of robots from a small bin of parts. We're gonna be building up to a really powerful formula that you can think...

Video [1:31] What happens if the director changes their mind and asks for two headed robots with different heads? How do you figure the combinations?

Tree diagrams allow us to visualize these counting problems using any number of parts. [0:48]

In this video (1:152) poses the question: How can trees be combined to count robots with many parts? Now, we need three kinds of parts; heads, bodies, and arms which can't be done with the table. See if you can combine the two diagrams...

Now it's your turn to drive. In this video [2:12] we'll present you with a casting challenge to complete using everything we've learned so far. Challenge: Build exactly 12 different robots with a total cost below $300.

This video [2:32] sets up a more difficult casting problem. How can we count the number of possible casts when given a large set of robots to choose from?

This video [1:52] mathematically answers the question "Does order matter?" when creating casts. To keep order from mattering, we need to take the total number of combinations where order does matter and divide that by all the possible...

Now it's time for a really meaty problem! How can we count the number of possible casts when given a large set of robots to choose from?

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

Let's review the multiplication principle which allows us to quickly count the number of possible robots.

Tree diagrams allow us to visualize these counting problems using any number of parts.

What happens if the director changes their mind and asks for two headed robots?

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

Why do we divide the number of combinations by the number of permutations?

This QuickTime movie provides practice using the fundamental counting principle with a variety of word problems. As you watch and listen to the teacher and students interact it helps clarify the thinking behind applying this concept.

This QuickTime movie provides a great introduction to the fundamental counting principle. A pdf worksheet is available by clicking on the hyperlink at the bottom of the page. As you watch and listen to the teacher and students interact...

This QuickTime movie demonstrates the meaning of factorials using a match type game. As you watch and listen to the teacher and student interact it helps clarify the thinking behind applying this concept.

This QuickTime movie provides another great activity to practice the fundamental counting principle using playing cards. As you watch and listen to the teacher and students interact it helps clarify the thinking behind applying this...