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# What is 2 factorial ?

Steps to calculate factorial of 2

To find 2 factorial, or 2!, simply use the formula that multiplies the number 2 by all positive whole numbers less than it.

Let’s look at how to calculate the Factorial of 2:

2! is exactly :
2
Factorial of 2 can be calculated as:
2! = 2 x 1

## What is Factorial?

In mathematics, factorial is a concept that involves multiplying a series of descending natural numbers. The factorial of 2, denoted as 2!, is simply the product of 2 and every natural number below it down to 1. Understanding the factorial of 2 is significant because it represents the simplest non-trivial case in combinatorial problems, serving as the foundation for understanding more complex factorial calculations.

## Formula to Calculate the Factorial of [Number]

The basic formula to calculate the factorial of any number “n” is given by:

n! = n × (n-1) × … × 1

Applying this to the number 2, we get:

2! = 2 × 1 = 2

This means that the factorial of 2 is 2.

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

Factorials play a crucial role in various mathematical domains, especially in combinatorics where they help in counting the number of ways things can be arranged. For instance, 2! is used to calculate permutations involving two distinct objects. In probability theory, it helps in determining the outcomes of events. Additionally, the unit of 2! is invaluable in computer algorithms, particularly in recursive functions and optimizations.

## Exercises

• How many ways can you arrange two books on a shelf?
• If a pair of dice is rolled, in how many ways can two sixes be rolled consecutively?

## Solutions to Exercises

1. There are 2! = 2 ways to arrange two books on a shelf.
2. Since only one outcome is sought (two sixes), there is only 1 way, not 2! = 2 ways, as permutations do not apply in this case.

### Q: Is the factorial of 2 used in algorithms?

Yes, the factorial of 2, while simple, is used in understanding recursive algorithms and forms a basic case for many algorithm optimizations.

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

In mathematics, 0! is defined as 1 to satisfy the property n! = n × (n – 1)!. When n=1, this gives the equation 1! = 1 × 0!, which can only be true if 0! = 1. This definition also aligns with combinatorial concepts where there is exactly one way to arrange zero items.