Permutations Calculator (nPr)
Calculate nPr, the number of ordered arrangements of r items chosen from n. Also shows nCr for comparison.
Permutations (nPr)
10P3 (order matters)
720
Number of ordered arrangements of 3 items chosen from 10.
For comparison: 10C3 (order does not matter)
120
Frequently Asked Questions about the Permutations Calculator (nPr)
What is a permutation?
A permutation is an ordered arrangement. nPr counts how many distinct sequences of length r you can build from n items, where order matters and items are not repeated.
How is nPr different from nCr (combinations)?
Permutations count ordered arrangements, combinations count unordered selections. For the same n and r, nPr = nCr times r factorial. Picking 3 winners with 1st/2nd/3rd place is nPr; picking 3 winners without ranking is nCr.
What is the formula for nPr?
nPr = n! / (n-r)! = n times (n-1) times ... times (n-r+1). Example: 10P3 = 10 x 9 x 8 = 720, while 10C3 = 720 / 6 = 120.
When should I use permutations in real life?
Whenever order matters: seating arrangements, race rankings, lock-code sequences, scheduling task orders, or assigning distinct roles to team members.
Why does the calculator switch to BigInt above n = 20?
21 factorial already exceeds JavaScript's safe integer range (2 to the 53). BigInt keeps results exact for large n and r instead of returning approximate doubles.