# What is 9 factorial ?

Steps to calculate factorial of 9

To find 9 factorial, or 9!, simply use the formula that multiplies the number 9 by all positive whole numbers less than it.

Let’s look at how to calculate the Factorial of 9:

## Factorials of Numbers similar to 9

## What is Factorial?

Factorial, symbolized by an exclamation mark (!), is a mathematical concept that represents the product of all positive integers from 1 up to a given number. The factorial of 9, denoted as 9!, is particularly significant in mathematics because it reflects the number of ways you can arrange or permute 9 distinct items. Understanding factorials is fundamental in various areas of mathematics, including combinatorics and probability theory.

## Formula to Calculate the Factorial of 9

The basic formula to calculate the factorial of a number n is *n! = n × (n-1) × … × 1*. Applying this formula to the factorial of 9, we follow these steps:

- Start with the number 9.
- Multiply 9 by every natural number less than itself down to 1.
- 9! = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1.

Following the calculation, the factorial of 9 equals 362,880.

## What is the Factorial of 9 Used For?

Factorials serve as a key tool in several mathematical fields. The factorial of 9, or 9!, has its applications in areas such as:

**Combinatorics:**Determining the number of possible combinations in a lottery or a card game.**Probability Theory:**Calculating the odds of certain events occurring within a fixed set of outcomes.**Algebra:**In the expansion of binomial expressions and solving series related problems.

These applications make the factorial of 9 a useful concept beyond theoretical math, extending into real-world scenarios and problem-solving.

## Exercises

- 1. Calculate the number of different ways to arrange 9 books on a shelf.
- 2. If 9 people are running in a race, how many different ways can the first three winners be chosen?

## Solutions to Exercises

- There are 9! or 362,880 different arrangements for the 9 books on a shelf.
- For the race with 9 runners, the first three winners can be chosen in 9!/(9-3)! or 9! / 6! ways, which is 9 × 8 × 7, or 504 different ways.

## Frequently Asked Questions

### Q: What is the value of 9 factorial?

A: The value of 9 factorial, or 9!, is 362,880.

### Q: Why is the factorial of 0 equal to 1?

A: By convention, the factorial of 0 is defined to be 1. This is because there is exactly one way (no way) to arrange zero objects, which reflects the base case for recursive definitions of factorials for all natural numbers.

## Other conversions of the number 9

9 in Roman numerals

9 in Spanich

9 in Italian