Permutations count arrangements where order matters, such as race finishing positions or PIN codes.
How to use the Permutation Calculator
- Total items (n)
- Items arranged (r)
Results update as you type, and every field accepts the units shown in its menu.
How it works
Divide n factorial by (n − r) factorial; with repetition, raise n to the power r.
Inputs explained
| Field | What to enter |
|---|---|
| Total items (n) | A number |
| Items arranged (r) | A number |
What each result means
- Permutations = perm([Total items (n)], [Items arranged (r)])
- With repetition (nʳ) = [Total items (n)]^[Items arranged (r)]
Formula
P(n, r) = n! ÷ (n − r)!With repetition: nʳWorked example
Inputs — Total items (n): 10; Items arranged (r): 3.
Results — Permutations = 720; With repetition (nʳ) = 1000.
Frequently asked questions
How many 4-digit PINs exist?
10⁴ = 10,000 with repetition.
How many ways can 3 medals go to 10 runners?
10 × 9 × 8 = 720.
What formula does the Permutation Calculator use?
P(n, r) = n! ÷ (n − r)!.