The last video in a three-part series on the Binomial Theorem from the Khan Academy. This segment illustrates how the Binomial Theorem is directly related to combinatorics using (a + b)^3 as an example. Students can clearly see how a...

Video explaining why we use the combinatorial formula for (n choose k) to expand binomial expressions. [11:58]

Tutorial provides an introduction to factorials. [5:28]

Video lesson solving for the probability of certain outcomes in four flips of a coin by finding the sample spaces and counting combinations. Includes link to additional practice problems. [10:00]

Video lesson deriving the formula for finding the probability of k heads in n flips.

Intuition behind why binomial expansion involves combinatorics. This segment illustrates how the Binomial Theorem is directly related to combinatorics using (a + b)^3 as an example. Students can clearly see how a binomial expansion...

Video showing how segmented snake toys can be used to explore some mathematical concepts.

The probability that at least 2 people in a room of 30 share the same birthday.

Probability of exactly 3 heads in 5 flips using combinations.

Today we're going to discuss the Binomial Distribution and a special case of this distribution known as a Bernoulli Distribution. The formulas that define these distributions provide us with shortcuts for calculating the probabilities of...

This video [1:53] asks the question: How do we keep track of how many robots we've made? You can learn more about what combinatorics is and how we use it at Pixar.

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?

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...

A different way to think about the probability of getting 2 heads in 4 flips.

Probability of getting exactly 3 heads in 8 flips of a fair coin.

Probability of getting a set of cards.

What is the probability of winning a 4-number lottery?