How to Calculate Permutations (nPr)

What is Permutations (nPr)?

Permutations (nPr) count the number of ordered arrangements of r items from n items. Order matters — ABC and BAC are different permutations of the same 3 letters.

Formula

P(n,r) = n! / (n−r)!

P: 5×4×3 = 60 — 5×4×3 = 60

Step-by-Step Guide

1P(n,r) = n! / (n−r)!
2Order DOES matter (unlike combinations)
3P(n,n) = n! — all n items in order
4P(5,3) = 5×4×3 = 60

Worked Examples

Input

Arrange 3 people from 8 in a row

Result

P(8,3) = 8×7×6 = 336 ordered arrangements

Frequently Asked Questions

What is Permutations?

Permutations (nPr) count the number of ordered arrangements of r items from n items. Order matters — ABC and BAC are different permutations of the same 3 letters

How accurate is the Permutations calculator?

The calculator uses the standard published formula for permutations. Results are accurate to the precision of the inputs you provide. For financial, medical, or legal decisions, always verify with a qualified professional.

What units does the Permutations calculator use?

This calculator works with inches. You can enter values in the units shown — the calculator handles all conversions internally.

What formula does the Permutations calculator use?

The core formula is: P(n,r) = n! / (n−r)!. Each step in the calculation is shown so you can verify the result manually.

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