Permutations (Jump to: Lecture | Video )

Imagine you’re visiting a zoo with six animals, and I ask you to record the first three animals you see. The six animals are:

Tiger, Lion, Monkey, Zebra, Walrus, Snake

How many different ways could you run into three animals?

Figure 1.

There are 6 animals you could record in the first spot. After that, there are only 5 animals left to see for the second spot. And after that, there are only 4 animals left to see for the final spot. When we multiply those three numbers, we find that there are 120 different ways you could run into three different animals. This is a permutation.

When I say that there are 120 different ways you could run into three different animals, I'm saying that order matters. For example, there are six different ways to run into the same three animals:

Tiger, Lion, Monkey

Tiger, Monkey, Lion

Lion, Monkey, Tiger

Lion, Tiger, Monkey

Monkey, Lion, Tiger

Monkey, Tiger, Lion

The permutations formula for this data would look something like this:

Figure 2.

But wait, what do the exclamation points(!) mean? Those mark factorials. Here are two examples of factorials:

6! = 6 * 5 * 4 * 3 * 2 * 1 = 720

4! = 4 * 3 * 2 * 1 = 24

In a factorial, you take the initial number and multiply it by every number between itself and one. So, our final answer for the first problem would look like this:

Figure 3.

As you can see, using the equation we still get an answer of 120.

Back to Top