🔀 Permutation Calculator
Calculate nPr permutations from n items
How Permutation Calculation Works
Formula
P(n, r) = n! / (n − r)!
- 1Enter the total number of items (n).
- 2Enter how many positions or items to arrange (r).
- 3The calculator computes n! and (n−r)! factorials.
- 4n! is divided by (n−r)! to get the number of arrangements.
- 5The result counts all possible ordered sequences.
About Permutation Calculator
Calculate permutations (nPr) — the number of ordered arrangements of r items from n. Shows step-by-step factorial calculations and explains when to use permutations vs combinations.
Frequently Asked Questions
When should I use permutations instead of combinations?
Use permutations when order matters — like ranking, passwords, seat arrangements, or race finishes. Use combinations when order doesn't matter — like choosing team members or lottery numbers.
What is P(n,n)?
P(n,n) = n!, the total number of ways to arrange all n items. For example, P(4,4) = 24, meaning 4 items can be fully arranged in 24 different orders.
How are permutations used in real life?
PIN codes (10⁴ = 10,000 four-digit combinations), license plates, phone numbers, seating arrangements, tournament brackets, and any scenario where the order of selection matters.