About this tool
Calculate the number of ordered arrangements when selecting r items from n items. This page explains the values requested and the method used so you can check whether the result fits your purpose.
How to use it
Enter Number of items (n) and Items selected (r).
Press Calculate, then review the result and the method below. Use Reset to clear the values in the calculator panel.
Method used
nPr = n! ÷ (n − r)!
Important assumptions and limits
Check that the units and values you enter are appropriate for your use case.
Maths note: Use consistent units and check the result against the method shown before relying on it.
Questions about this result
Are the values I enter sent to The Decimal Space?
No. This calculator processes the values in your browser. This page does not require a calculator account or a server-side save function.
Can I use this for an important decision?
Check the inputs, units, formula and any rounding. For a decision with legal, tax, financial, medical, engineering or safety consequences, use an official source or obtain advice from an appropriately qualified professional.
Why might a result differ from another calculator?
Different tools can use different inputs, rounding, units, assumptions or formulas. Compare the calculation method rather than relying only on a displayed number.