The factorial n! is the product of all whole numbers from 1 to n: 5! = 5 x 4 x 3 x 2 x 1 = 120, and 0! is defined as 1. A permutation counts ordered selections: nPr = n! / (n - r)!. A combination counts selections where order does not matter: nCr = n! / (r! x (n - r)!).
Example: choosing 3 people from 10 for gold, silver and bronze (order matters) gives 10P3 = 720. Choosing 3 people for a committee (order does not matter) gives 10C3 = 120.
Up to 1000. Results use exact whole-number math, so nothing is rounded, though very long results are shown with their digit count and leading digits.
1. There is exactly one way to arrange zero items.
You cannot choose more items than exist, so nPr and nCr are shown as a dash if r > n.
See also: prime number checker · GCF and LCM calculator · exponent calculator