How is permutation different from combination?

In permutations, order matters (ABC ≠ BAC). In combinations, order does not matter (ABC = BAC = CBA). Combinations are smaller: C(n,r) = P(n,r) / r!.

When do I use permutations?

Use permutations when order matters: ranking contestants (1st, 2nd, 3rd place), arranging books on a shelf, creating passwords, or scheduling event sequences.

P(n, n) = n! — the total number of ways to arrange all n items. For example, P(5,5) = 5! = 120 ways to arrange 5 books.

Permutation Calculator — nPr

The Permutation Calculator computes P(n, r) — the number of ways to arrange r items chosen from a set of n items, where order matters. Permutations are used in combinatorics, probability, scheduling, and any situation where the arrangement or sequence is important.

Total items (n)

Items chosen (r)

Frequently Asked Questions

A permutation is an ordered arrangement of items. P(n, r) = n! / (n-r)! gives the number of ways to arrange r items from n, where order matters. P(5,3) = 60.

Related Calculators

🧮Combination Calculator 🧮Factorial Calculator 🧮Probability Calculator