nPr Permutation Calculator P(n,r)

P(n, r) Result

What is a Permutation?

A permutation is an ordered arrangement of items. P(n,r) gives the number of ways to arrange r items chosen from n items, where the order matters.

P(n, r) = n! / (n − r)!
P(10, 3) = 10! / 7! = 10 × 9 × 8 = 720

When Order Matters: Use Permutations

  • Number of ways to arrange 3 people in 3 seats from 10 people
  • First, second, third place in a race from 8 runners
  • 4-digit PIN codes from 10 digits (with repetition not allowed)

Frequently Asked Questions

What is P(5,2)? ▼
P(5,2) = 5!/(5−2)! = 5!/3! = 5×4 = 20. There are 20 ordered ways to choose 2 items from 5.
What is the difference between permutation and combination? ▼
In permutations, order matters (ABC ≠ BCA). In combinations, order does not matter (ABC = BCA). Use permutations for rankings, arrangements; combinations for selections, groups.
What is P(n,n)? ▼
P(n,n) = n!/0! = n!/1 = n!. It gives the number of ways to arrange all n items, which equals n factorial.