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Calculators > Permutation Calculator / Combination Calculator

Watch the video or scroll down for the calculator.



The “Mathy” Way

n =

r =

Does the order matter? Yes No

Can the items repeat? Yes No



When the order of items matters, that’s called a Permutation.

When the order of items doesn’t matter, that’s called a Combination. Since we are not allowed to repeat items, we use the following formula:

Number of possible Permutations = nr = = Number of possible Permutations = n! (n – r)! = ! ( – )! = Number of possible Combinations = (n + r – 1)!

r!(n – 1)! = ( + – 1)! !( – 1)! = Number of possible Combinations = n! r!(n – r)! = ! !( – )! = Since we areallowed to repeat items, we use the following formula:

The Visual Way

A form of the permutation problem that students commonly see is the “committee” problem. For example:

If there are 5 people, Jim, Jane, Bob, Susan, and Ralph, and only 3 of them can be on the new PTA committee, how many different combinations are possible?

In this example, there are 5 people to choose from (so n equals 5), and we need to choose 3 of them (so r equals 3).

Order doesn’t matter: if Jim is on the committee, he’s on the committee whether he’s picked first or last. Repetition isn’t allowed because Susan can’t be on the committee twice (even if she really wants to be!)

So, if we use the “mathy” way from above, we know the formula is:

Number of possible Combinations = n! r!(n – r)!

And we input the number 5 for n, and 3 for r, and so we know that there 10 possible combinations. But what does that actually mean?

Combinations Generator

I’ll show you using our generator:



Jim, Jane, Bob, Susan, Ralph How many are you picking?

Does the order matter? No.

No. Can the items repeat? No. All possible items:

Possibilities:







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