🔢Permutation Calculator

Calculate the number of permutations P(n,r) for ordered arrangements.

n (total items)

r (items to arrange)

P(10,3) = 10! / (10-3)!

720

The number of ordered arrangements of 3 items from 10

About Permutation Calculator

Calculate the number of permutations P(n, r) — the number of ways to arrange r items chosen from a set of n items where order matters. Enter n (total items) and r (items to arrange) and get the result with step-by-step factorial calculation shown.

How to Use Permutation Calculator

1
Enter n and r
Input the total number of items (n) and how many you want to arrange (r).
2
Calculate
Click Calculate to get P(n, r) with the factorial formula shown step by step.
3
Use the result
Apply the permutation count to probability and combinatorics problems.

Common Use Cases

Counting possible race finishing orders
Calculating password combination counts
Solving combinatorics exam problems
Analysing arrangement possibilities in scheduling

Frequently Asked Questions

What is a permutation?

A permutation is an ordered arrangement of items. P(n, r) = n! / (n-r)! counts the number of ways to choose and arrange r items from n total items where the order matters (e.g. 1st, 2nd, 3rd place in a race).

What is the difference between permutations and combinations?

In permutations, order matters (ABC ≠ BAC). In combinations, order does not matter (ABC = BAC). Use the Combination Calculator when order is irrelevant.