Permutation Combination Calculator: Does Order Matter?

Permutations and combinations answer the same question differently: permutations care about order, combinations do not. Knowing which you need is half the problem.

What is the Permutation Combination Calculator?

Enter n (the total items) and r (the items chosen), and the tool calculates both: permutations, where order matters, and combinations, where it does not. For example, choosing a president and a secretary from 10 people is a permutation, while choosing a 3-person team is a combination.

How to use it

1. Enter n, the total number of items.
2. Enter r, the number chosen.
3. Click Calculate P and C for both answers.

Worked example

Choosing 3 from 10 gives 720 permutations (order matters) and 120 combinations (order does not), since 720 divided by 3 factorial, which is 6, equals 120.

When do I use permutations?

When order matters, such as ranking first, second, and third, or filling distinct roles like president and secretary.

Frequently asked questions

When do I use combinations?

When order does not matter, such as picking a team where every member has the same role.

Why is C smaller than P?

Because each combination can be ordered in r factorial ways, and combinations count those orderings only once.

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