Permutation
Definition
An ordered arrangement of objects. The number of permutations of n objects taken r at a time is P(n,r) = n! / (n-r)!.
Why is Permutation Important?
Permutation is a foundational mathematical concept used across science, engineering, finance, and everyday problem-solving. From analyzing data sets to optimizing business decisions, this concept provides the analytical framework needed to interpret quantitative information accurately.
Our math calculators make complex computations simple and accessible, providing step-by-step results that help students, professionals, and curious minds explore mathematical relationships with confidence.
What is a Permutation?
A permutation is an ordered arrangement of objects. The number of permutations of n objects taken r at a time is the number of distinct sequences that can be formed. Order matters in permutations โ ABC is different from BAC.
Permutation Formula
P(n, r) = n! / (n โ r)!
Examples
| Problem | Formula | Result |
|---|---|---|
| Arrange 5 books on a shelf | P(5,5) = 5! | 120 arrangements |
| Choose President, VP, Secretary from 10 people | P(10,3) = 10!/7! | 720 ways |
| 4-digit PIN (digits 0-9, no repeat) | P(10,4) = 10!/6! | 5,040 codes |
| First 3 finishers in a 20-person race | P(20,3) = 20!/17! | 6,840 outcomes |
Permutation vs Combination
| Feature | Permutation | Combination |
|---|---|---|
| Order | Matters (AB โ BA) | Doesn't matter (AB = BA) |
| Formula | n!/(nโr)! | n!/(r!(nโr)!) |
| Choosing 3 from 5 | 60 | 10 |
| Examples | Rankings, PINs, seating charts | Committees, lottery, teams |