Compute nPr, factorial, circular, repeated, and multiset cases. See steps, checks, and example outputs instantly. Download clean reports for classwork, revision, and quick verification.
| Case | Input | Formula | Output |
|---|---|---|---|
| Standard permutation | n = 8, r = 3 | 8! / 5! | 336 |
| Full permutation | n = 6 | 6! | 720 |
| Repetition allowed | n = 4, r = 3 | 4^3 | 64 |
| Circular permutation | n = 7 | 6! | 720 |
| Multiset permutation | counts = 3, 2, 1 | 6! / (3! × 2! × 1!) | 60 |
Standard permutation without repetition: P(n, r) = n! / (n - r)!
Full permutation of all distinct items: n!
Permutation with repetition allowed: n^r
Circular permutation: (n - 1)!
Multiset permutation: n! / (a! b! c! ...)
In these formulas, n means total available items. r means selected positions. The factorial symbol means repeated multiplication down to 1.
This discrete math permutation calculator helps you count ordered arrangements. Order matters in every permutation problem. That is the key idea. The tool covers the most common classroom and exam cases. You can solve standard nPr questions. You can also solve full arrangement questions. It also handles circular arrangements. It supports repetition cases too. Multiset inputs are included for repeated objects. This makes the page useful for school, college, and revision work.
Permutation formulas appear in many maths topics. They show up in counting principles. They support probability questions. They also help with coding theory and seating plans. You may need them for password patterns. You may use them in tournament order analysis. They are common in discrete structures courses. They are also important in combinatorics. A strong calculator saves time. It also reduces manual factorial mistakes.
The standard mode finds ordered selections without reuse. The full mode finds all possible arrangements of distinct items. The repetition mode counts ordered strings when reuse is allowed. The circular mode removes duplicate rotations. That is useful for round tables and ring layouts. The multiset mode handles repeated symbols or objects. This is important when some items are identical. Each result includes a formula summary. You also get input checks and optional worked steps.
This page is built for quick checking and concept review. The example data table shows solved sample cases. The formula section explains what each model means. The how-to section keeps the workflow simple. The result area appears above the form after submission. That makes checking faster on desktop and mobile screens. Export buttons help you save work. Use CSV for tabular review. Use PDF for printable notes. Together, these features make permutation practice clearer, faster, and more accurate.
A permutation counts ordered arrangements. A combination counts selections where order does not matter. If position changes the outcome, use a permutation formula.
Use P(n, r) when you choose r items from n distinct items and order matters. This is common in rankings, seat assignments, and code arrangements.
Use full permutation when every distinct item is arranged. In that case, the answer is n!, because all available items are placed in order.
In a circle, rotating the same arrangement does not create a new one. Fixing one item removes repeated rotations, so the count becomes (n - 1)!.
It means each position can reuse the same choice. If there are n possible choices for each of r positions, the total count is n^r.
A multiset permutation is used when some items are identical. You divide by repeated-group factorials to remove duplicate arrangements from the total factorial count.
Yes. This file uses exact integer-style string multiplication for supported limits. That helps avoid floating-point rounding errors in large permutation outputs.
Yes. The result section includes CSV and PDF buttons. CSV saves the table data, and PDF creates a clean printable copy of the result block.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.