What is 15 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.

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.

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.

• 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?

• 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.