# How to Use Factorial Notation: Process and Examples

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• 0:47 What It Means
• 1:41 Dividing Factorials
• 3:11 More Examples
• 3:51 Lesson Summary

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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson to learn about factorial notation. Understand what it means so that you can handle it like a pro. Also see what happens when we divide factorials.

## The Factorial Notation

What does the exclamation mark mean to you? We usually use it to make a statement such as 'Hey man, I got this!' Well, guess what? We also have a use for this mark in math. We call it 'factorial notation.' The factorial notation is the exclamation mark, and you will see it directly following a number. For example, you will see it as 5! or 3!. You read these as 'five factorial' and 'three factorial.' You will see your factorial notation when doing problems that ask you about the number of possible combinations. For example, factorial notation is used to find how many different ways you can arrange a blue marble, a red marble, and a green marble.

## What It Means

What does this factorial notation mean? Factorial means that we multiply all the integers less than or equal to our chosen number. So, 5! means that we multiply five times four times three times two times one, 5*4*3*2*1, all the numbers less than or equal to our chosen number. Do you see how we just started with our 5 and kept multiplying it with the numbers we use to count down all the way to 1? This is what factorial is about. So, 3! is three times two times one, 3*2*1. We just multiply it out and we have what our factorial equals. So, 5! equals 120, and 3! equals 6.

So, you can think of the factorial as telling you that 'you've got this!,' that you've got all the numbers less than or equal to your chosen number!

## Dividing Factorials

Now, what happens when we divide factorials? Like, what happens when we divide five factorial by three factorial, 5!/3!? Well, let's see. First, we write out what each factorial means. So, we have 5*4*3*2*1/3*2*1. Well, now we see that there are some things we can cancel out since we have the same number in the numerator AND the denominator. We can cancel out the threes and the twos and the ones. So, we are left with 5*4. Well, isn't that interesting? Our problem got a lot simpler. We know that 5*4 equals 20, and we are done.

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