# What is 10 factorial ?

Steps to calculate factorial of 10

To find 10 factorial, or 10!, simply use the formula that multiplies the number 10 by all positive whole numbers less than it.

Let’s look at how to calculate the Factorial of 10:

## Factorials of Numbers similar to 10

## What is Factorial?

In mathematics, the factorial of a non-negative integer is the product of all positive integers less than or equal to that number. It’s symbolized by an exclamation point (n!). Understanding the factorial of 10 is significant because it represents the total number of ways that 10 distinct items can be arranged in sequence, which is foundational for permutations and combinations, essential concepts within probability and combinatorial theory.

## Formula to Calculate the Factorial of [Number]

The factorial of a number (n!) is calculated using the formula **n! = n × (n-1) × … × 1**. For the number 10:

10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

Applying this step by step, we obtain the factorial value of 10:

10! = 3,628,800

## What is the Factorial of [Number] Used For?

The factorial function has several intriguing applications, particularly the factorial of 10. It is used in:

- Combinatorics, to calculate the number of possible combinations or permutations in a set.
- Probability theory, to determine the chances of an ordered sequence of events occurring.
- Statistics, during calculations involving distributions or samples.

The factorial of 10 plays a notable role in arranging 10 unique objects or selecting subsets from a larger group.

## Exercises

- Calculate the number of ways you can arrange 10 different books on a shelf.
- If you have to choose 3 appetizers from a menu of 10, how many different combinations can you create?

## Solutions to Exercises

- The number of ways to arrange 10 books is equal to 10 factorial (10!). This is 10! = 3,628,800 ways.
- For 3 appetizers out of a menu of 10, the number of combinations is calculated using the formula 10! / [7! × (10-3)!], giving a total of 120 combinations.

## Frequently Asked Questions

### Why is the factorial of zero equal to one?

Mathematically, 0! is defined as 1 because there is exactly one way to arrange zero objects (by doing nothing with them), which adheres to the convention of an empty product.

### Is the factorial function applicable only to whole numbers?

Yes, factorials are defined only for non-negative whole numbers. For non-integer and negative numbers, the gamma function extends the concept.

### How do you calculate factorials for large numbers?

For very large numbers, factorials are often computed with software that use sophisticated algorithms to handle the large integer calculations efficiently.

## Other conversions of the number 10

10 in Roman numerals

10 in Spanich

10 in Italian