Permutations and Factorials
Permutations and factorials are fundamental concepts in combinatorics, the branch of mathematics dealing with counting and arrangement possibilities.
Factorial of a non-negative integer n, denoted as n!, is the product of all positive integers less than or equal to n. Mathematically it is represented as:
n! = n × (n-1) × (n-2) × (n-3) × (n-4)…….. × 1
A permutation is an arrangement of a set of objects in a specific order. The concept is essential when the order of arrangement matters.
For example: Number of ways to arrange 3 objects (A, B, C) is 3! = 6 (ABC, ACB, BAC, BCA, CAB, CBA).
Zero Factorial (0!)
The value of zero factorial is 1. Factorial of any number “n” is calculated by multiplying all the numbers between n and 1 (including n). So one might ask what is the value of zero factorial, the value of 0! factorial is 1 and this is calculated using various methods.
In this article we are going to learn about the definition of factorial, how factorial is calculated, the Derivation of 0! is equal to 1, Examples and FAQs related to Factorial, and others.
Table of Content
- Definition of Factorial
- How is Factorial Calculated?
- What is Factorial of 0?
- Derivation of Zero Factorial is Equal to 1
- Permutations and Factorials
- Factorial of Negative Number
- Operations On Factorial
- Sample Problems on Zero Factorial
- Practice Problems on Zero Factorial
- Zero Factorial – FAQs