Permutation Calculator
Use this permutation calculator when the order of selected items matters. Calculate nPr without repetition or allow repetition for ordered selections where an item may be used more than once. Results use exact integer arithmetic.
How to use the Permutation Calculator
- Enter the total number of available items n.
- Enter how many items r will be selected or arranged.
- Choose whether repetition is allowed.
- Without repetition, the calculator uses n! divided by (n − r)!.
- With repetition, the number of ordered sequences is n raised to the power r.
Examples
10 choose 3 where order matters
10P3 = 10 × 9 × 8 = 720 possible ordered arrangements.
PIN-style arrangement
If 10 possible digits can be used in each of 4 positions with repetition, there are 10⁴ = 10,000 ordered sequences.
Permutation versus combination
ABC and CBA count as different permutations because their order is different.
Frequently asked questions
What is a permutation?
A permutation is an arrangement where order matters. Changing the order creates a different outcome.
What is nPr?
nPr represents the number of ways to arrange r items selected from n distinct items without repetition.
What is the difference between a permutation and combination?
Permutations treat different orders as different outcomes. Combinations count only which items are selected, regardless of order.
Can permutations allow repetition?
Yes. When repetition is allowed and there are n choices for each of r positions, the count is n raised to r.
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