Permutation Calculator (nPr)
Enter how many items you have and how many you arrange. Order matters, so ABC and CBA count as different.
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Formula
nPr = n! ÷ (n - r)! which is the product n × (n-1) × ... × (n-r+1)
Worked example
Arrange 3 of 10 items: 10P3 = 10 × 9 × 8 = 720. Arrange 4 of 10: 10 × 9 × 8 × 7 = 5,040.
A larger case: 25P20 = 1.292601 × 10^23 (24 digits). Results above 9,007,199,254,740,991 are shown as 7 significant digits plus the exact digit count rather than a made-up exact integer.
Frequently asked questions
What is the permutation formula?
nPr = n! ÷ (n - r)!. For 5P3 that is 5 × 4 × 3 = 60 ordered arrangements.
What is the difference between a permutation and a combination?
In a permutation order matters, in a combination it does not. 10P4 = 5,040 while 10C4 = 210, which is 5,040 ÷ 4!.
What is nPr when r is 0 or equal to n?
nP0 is 1, since there is one way to arrange nothing. nPn is n!, so 6P6 = 720.
Why is n limited to 170?
170! is about 7.26 × 10^306, the largest factorial a standard double-precision number can hold. Above that the result overflows, so larger values are rejected. Answers are computed exactly with integer arithmetic. Up to 9,007,199,254,740,991 they are shown in full; larger ones are shown as 7 significant digits, such as 25P20 = 1.292601 × 10^23, together with the exact number of digits.