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)

How to Use This Calculator

1
Enter n — the total number of items in the set.
2
Enter r — the number of items you are arranging.
3
Click Calculate to see the number of permutations.

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