Today we are going to learn how to **calculate factorials.** Calculating factorials is quite simple; let’s see what it’s all about:

##### What is the Factorial Function?

We represent the factorial function with the exclamation point **“!”**, placing it behind the number. This exclamation means that we need to multiply all of the positive whole numbers that fall between the number and 1.

**For example:**

We generally say “6 factorial”, although it can also be “factorial of 6”.

On your calculator, you’ll see a button with “n!” or “x!”. You can use this button to calculate the factorial of whatever number that you want to calculate.

##### A Few Examples of Factorials

We’re going to take a look at some more examples of factorials:

As you can see, 100! is a huge number…

And, what do we do with the smaller numbers? 1 factorial is, logically, 1, because it’s simply 1 x 1:

But, how can we calculate the 0 factorial? Well, when we apply the norms of multiplying all of the positive whole integers that fall between 0 and 1, it doesn’t make sense to calculate it because 0 x 1 is 0.

So, the solution is to equate the 0 factorial to 1. So, just remember that:

##### What do we use factorials for?

Above all, the factorial numbers are used in combinatorial analysis, in order to calculate** combinations and permutations**. In combinatorial analysis, factorials can also be used to calculate probabilities.

We are going to take a look at a simple problem where we can apply factorials.

**Paula took out the 4 aces from a deck of cards. She is going to put them in a line on the table. How many different ways could she line them up?**

In this problem, we have to solve a “**permutation**”, or in other words, we have to find out all of the possible ways that these 4 cards can be ordered.

If we start by making all of the possible lines that start off with the ace of diamonds, we can make 6 combinations:

We’ll also have 6 possible combinations with the ace of clovers, hearts and spades. In other words, 6 combinations starting with each one of the 4 aces: **4 x 6 = 24**

**She could order them in 24 different ways.**

Using the factorial function, we could have solved the problem through a much simpler way:

If you start with only one combination of the 4 aces:

- When we choose the first one, there are only 3 left to choose from
- When we choose the second one, there are only 2 left to choose from
- Then when we choose the third one, there is only 1 left to choose from

So as a result, all of the possible combinations are **4 x 3 x 2 x 1.**

It’s the same thing as **4! = 24**

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