Permutation Calculator (nPr)

Use permutations when order matters: podium finishes, PIN codes, seating plans.

Permutations

Permutations P(n, r)720

Working

  1. P(n, r) = n! ÷ (n − r)! = 10! ÷ 7!

Formulas

without repetition: nPr = n! ÷ (n − r)!

with repetition: nr

Worked example

Gold, silver and bronze among 10 runners

  1. n = 10, r = 3, no repetition
  2. 10! ÷ 7! = 10 × 9 × 8

720 possible podiums.

A 4-digit PIN

  1. n = 10 digits, r = 4, repetition allowed
  2. 10⁴

10,000 possible PINs.

Permutation or combination?

If swapping the chosen items gives a different result, it is a permutation. Choosing a president, secretary and treasurer is a permutation; choosing a committee of three is a combination. For the same n and r, nPr = nCr × r!.