What Is a Permutation?
Definition
Permutation: An arrangement of r items from n different items in which the order matters. Their number is P(n, r) = n! / (n − r)!; 9 swimmers can finish first, second and third in 504 ways.
A permutation is an arrangement of r items from n different items in which the order matters: AB and BA are two arrangements. Permutations count race places, the assignment of roles and codes. Nine swimmers can finish first, second and third in 504 ways, and all nine can line up in 362,880 ways.
Where it appears in the formulas
P(n, r) = n! / (n − r)!, also written nPr. The permutations calculator uses it: P(9, 3) = 362,880 / 720 = 504. With repetition, when an item can fill every place again, the count is nʳ: a 4-digit PIN has 10⁴ = 10,000 possible values.
How it differs from a combination
In a combination the order does not matter, so the r! orders of the same r items count as one choice: C(n, r) = P(n, r) / r!.