Permutation Calculator (nPr): Arrangements Where Order Matters
Enter n and r. You get the number of ordered arrangements nPr as an exact whole number, with the factors multiplied out.
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Result
720
- Number of digits
- 3
Permutations count ordered arrangements: AB and BA are different.
Show working
- ⁿPᵣ = n! / (n − r)!
- = 10! / 7!
- = 10 × 9 × 8
- = 720
How to use
- Enter n, the total number of items.
- Enter r, how many are arranged.
- Choose whether repetition is allowed and read nPr.
Good to know
Formula: nPr = n!/(n − r)! = n × (n − 1) × … × (n − r + 1). For example, the number of ways to award gold, silver and bronze among 10 runners is 10P3 = 10 × 9 × 8 = 720.
With repetition (like a 4-digit PIN from 10 digits) every position has n choices, so the count is nʳ = 10⁴ = 10,000.
Results use exact big-integer arithmetic, so 100P50 is given to all 94 digits, not rounded. Very long answers are shown in scientific form, with the full number in the working.
Questions
What is the difference between permutation and combination?
In a permutation the order matters (ABC ≠ BAC); in a combination it does not. nPr = nCr × r!.
What is 5P2?
5 × 4 = 20.
What is 0! and nP0?
0! = 1 by definition, so nP0 = 1: there is one way to arrange nothing.
How many arrangements of the letters of “INDIA”?
With repeated letters divide by the repeats: 5!/2! = 60, because I appears twice.
Is my data stored or sent anywhere?
No. The calculation runs entirely in your browser; nothing you type leaves your device.