Combination Calculator

Combination Calculator

Calculate combinations, permutations, and factorial values with strict integer validation.

Last updated: 2026-06-21T07:59:22.026Z

Enter integers with 0 less than or equal to r less than or equal to n less than or equal to 1000.

Results

Combinations

C(10,3) = 120

Permutations

P(10,3) = 720

10!

3628800

3!

6

What are combinations and permutations?

Combinations count ways to choose items where order does not matter. Permutations count ways to arrange items where order does matter.

Formula reminders

Combination formula

C(n,r) = n! / (r!(n-r)!)

Permutation formula

P(n,r) = n! / (n-r)!

Worked example

Choose 6 from 49

C(49, 6) = 13,983,816

P(49, 6) is the matching permutation example for the same inputs.

For a separate quick check: P(8, 3) = 336.

Frequently asked questions

When do I use combinations?

Use combinations when order does not matter.

When do I use permutations?

Use permutations when order matters.

Can r be larger than n?

No. In this calculator that is treated as invalid input.

Why is 0! equal to 1?

It keeps counting formulas consistent.

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