What Are Permutations?
Permutations are a fundamental concept in mathematics, particularly in the field of combinatorics. They involve the arrangement of items in a specific order.
Mathematical Formulation
The number of permutations of n distinct objects is given by the factorial of n, denoted as n!.
n! = n × (n - 1) × (n - 2) × ... × 1
Example Calculation
If you have 4 letters (A, B, C, D) and want to find out how many ways you can arrange 2 of them:
P(4, 2) = 4! / (4 - 2)! = 12
Applications of Permutations
Permutations have a wide array of applications across various fields, including mathematics, computer science, cryptography, and game theory.