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# What is 12 factorial ?

Steps to calculate factorial of 12

To find 12 factorial, or 12!, simply use the formula that multiplies the number 12 by all positive whole numbers less than it.

Let’s look at how to calculate the Factorial of 12:

12! is exactly :
479001600
Factorial of 12 can be calculated as:
12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

## What is Factorial?

A factorial, represented by an exclamation point following a number, is a product of all positive integers less than or equal to that number. The factorial of 12, denoted as 12!, is of substantial importance in mathematics, particularly in the realm of combinatorics and probability. Understanding the factorial of 12 is crucial for arranging items in sequences, calculating permutations, and figuring out the probability of events in complex scenarios.

## Formula to Calculate the Factorial of 12

The formula for calculating the factorial of a number is:

n! = n × (n-1) × … × 1

Now, let’s calculate the factorial of 12 step by step:

12! = 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

This results in 12! equaling 479,001,600.

## Applications of the Factorial of 12

The factorial of 12 has several fascinating applications:

• Combinatorics: Determining the number of possible combinations of 12 different items.
• Probability Theory: Calculating the odds of specific outcomes when 12 options are available.
• Algebra: Simplifying expressions and solving equations involving factorials.

## Exercises on Factorial of 12

Try these exercises to deepen your understanding of factorials:

• 1. How many different ways can a dozen eggs be arranged in a carton?
• 2. If you have 12 shoes, in how many ways can you pair them up?
• 3. What is the ratio of arrangements for 12 items to arrangements for 10 items?

## Solutions to Exercises

Here are the answers to the exercises provided earlier:

1. 479,001,600 ways.
2. 479,001,600 ways.
3. The ratio of arrangements for 12 items to 10 items is 479,001,600 to 3,628,800, simplifying to 132.

### What exactly is the factorial of 12?

The factorial of 12, written as 12!, represents the product of all positive integers from 1 to 12 and is equal to 479,001,600.

### Can the factorial of 12 be used in real-life applications?

Yes, understanding and computing the factorial of 12 can be applied to various real-life situations, especially in scenarios requiring the arrangement or combination of 12 different elements.

### Is the factorial of 12 relevant in computer science?

Absolutely, in computer science, the factorial of 12 can be useful for algorithms involving combinatorial problems or when calculating the complexity of certain algorithms.