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# What is 15 factorial ?

Steps to calculate factorial of 15

To find 15 factorial, or 15!, simply use the formula that multiplies the number 15 by all positive whole numbers less than it.

Let’s look at how to calculate the Factorial of 15:

15! is exactly :
1307674368000
Factorial of 15 can be calculated as:
15! = 15 x 14 x 13 x 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?

The factorial of a number, denoted as n!, represents the product of all positive integers from n down to 1. It’s a concept that has a significant impact in various branches of mathematics, and it’s particularly intriguing when looking at higher numbers like 15. Understanding the factorial of 15 provides insight into arrangements and combinations possible within a set number of objects, elucidating countless mathematical and statistical principles.

## Formula to Calculate the Factorial of 15

To calculate the factorial of 15, we start with the basic factorial formula: `n! = n × (n-1) × ... × 1` and apply it to 15:

• 15! = 15 × 14 × … × 1

Following this all the way to 1, you multiply all numbers in this range to get the factorial of 15, which is a quite large number:

15! = 1,307,674,368,000.

## What is the Factorial of 15 Used For?

The factorial function, and 15! in particular, have fascinating applications. In combinatorics, it’s used to determine the number of ways to arrange or combine different elements. In probability theory, it’s employed when calculating permutations. The factorial of 15 is significant when dealing with complex problems where 15 different elements can lead to a vast number of potential outcomes.

## Exercises

• If you have 15 different books, in how many ways can you arrange them on a shelf?
• Out of a team of 15 players, in how many ways can you select a captain and vice-captain?

## Solutions to Exercises

• The books can be arranged in 15! = 1,307,674,368,000 different ways.
• For captain and vice-captain, the result would be 15 × 14 taken 2 at a time, which is 210 different possibilities.

### Q: What is the exact value of 15 factorial?

The exact value of 15 factorial (15!) is 1,307,674,368,000.

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

0 factorial is defined as 1 because there is exactly one way to arrange zero objects, which is to have no arrangement at all.

### Q: Can negative numbers have a factorial value?

No, factorials are only defined for non-negative integers. The factorial of negative numbers is undefined.