## What is a factorial?

A factorial calculates the ‘product’ of all numbers less than or equal to a value. For example, the factorial of 5 would be:

**5x4x3x2x1=120**

In mathematical notation, factorials are usually indicated with an exclamation mark. **5!** would indicate the factorial of 5.

Factorials are typically used to calculate a number of possible combinations (or permutations). For example, the British National Lottery sells lottery tickets that contains 6 numbers from 1 to 59. The mathematical formula to calculate the total possible combinations of numbers is:

**59!/(6!*(59-6)!)**

This results in a value of **45,057,474**, showing that a single ticket has a 1 in 45,057,474 chance of winning the British National Lottery!

## Factorials in Excel

Because the exclamation mark is the symbol for a factorial you might expect it to be recognized by Excel, but you will get an error message if you try to enter a formula such as **=5!**.

To calculate factorials in excel you must use the **FACT** function.

**=FACT(5)** would calculate the factorial of 5 in Excel.

If you’re unfamiliar with Excel formulas and functions you could benefit greatly from our completely free Basic Skills E-book.

Many more advanced functions are explained in depth in our Expert Skills Books and E-books.

## Calculating the probability of winning the lottery in Excel

Now that you know how to use the FACT function, it’s a simple matter to translate the mathematical formula shown above into an Excel formula:

**=FACT(59)/(FACT(6)*FACT(59-6))**

You can download an example workbook showing this in action.

## Other combinatorial functions in Excel

Excel also contains a number of other useful ‘combinatorial’ functions. One of the most useful is **COMBIN**. COMBIN makes the calculation shown above even easier, as it allows you to return the total number of possible combinations from a given number of items. You can calculate the probability of winning the lottery with the simple formula:

**=COMBIN(59,6)**

Excel also offers the **COMBINA** function, which works the same way but allowing repetition of numbers. If you were allowed to choose the same number more than once in the lottery there would be *74,974,368 *possible combinations and it would be much harder to win!