Combinatorics calculator

Permutation Calculator

Find how many ordered arrangements contain r items selected from n available items.

Enter values and select Calculate.

Formula and method

For 0 ≤ r ≤ n, P(n,r) = n! / (n−r)!. The engine multiplies n × (n−1) × … × (n−r+1) with BigInt, so every supported result remains exact.

Worked example

Arranging 3 positions from 10 items gives P(10,3) = 720. Order matters, so this differs from choosing an unordered group.

Inputs and boundaries

n and r must be nonnegative integers, with r no greater than n.
The calculation is without repetition.
Inputs are limited to 10,000 to prevent pathological browser work.
The full exact integer is returned; no floating-point precision is lost.

Inputs and results stay in this browser and are not sent to analytics, storage, URLs, or network services.