Permutation

A permutation is a specific ordering or arrangement of a set of objects, elements, or symbols. It represents a distinct sequence where the order of the items is significant. The number of possible permutations of a set depends on the number of items and whether repetition is allowed. Permutations are fundamental concepts in combinatorics and are widely used in probability, statistics, computer science, and various fields involving arrangement and sequencing.

Permutation meaning with examples

• Consider the letters 'A', 'B', and 'C'. The permutations are ABC, ACB, BAC, BCA, CAB, and CBA. Each arrangement is unique based on the order. The factorial function (3!) calculates the number of permutations for 3 objects.
• A password uses a permutation of characters where order dictates security. Changing the order of your password elements changes it to a different password, providing security because an attacker cannot just guess what is included, but also has to get the order correct.
• In a race with 5 runners, the finishing order is a permutation. If three spots are awarded on the podium, how many permutations of top three finishers are possible based on their sequence when crossing the finish line.
• A permutation is used to define the optimal seating arrangements. A theater may utilize seating arrangements which may be a permutation of the possible seating arrangements based on certain requirements such as seating together certain families.