Math

Permutation and Combination Calculator

Use OmniCalc's permutation and combination calculator to count possible selections when order matters or does not matter.

Permutation and combination calculator

Count selections with or without order.

Enter the total number of items, how many are selected, and whether order matters to calculate combinations or permutations instantly.

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Why this result matters

What this calculator helps you answer

A distinct combinatorics page that broadens the math/stats wedge beyond inference into counting problems with strong classroom and exam intent. Use the tool above to enter a few clear inputs and get a practical answer you can use right away.

This permutation and combination calculator helps students quickly compute nCr and nPr values without expanding factorial formulas by hand. Enter the total number of items, the number selected, and whether order matters to get the answer instantly.

Formula and method

How the calculation works

For combinations, the calculator uses nCr = n! / (r! × (n-r)!). For permutations, it uses nPr = n! / (n-r)!.

Example

Example combinatorics calculation

If you choose 3 items from 10, there are 120 combinations when order does not matter and 720 permutations when order matters.

FAQ

Common questions about this calculator.

Short answers to the questions people often ask before or after using the tool.

Question

What is the difference between combinations and permutations?

Combinations ignore order, while permutations count different orders as different outcomes.

Question

When should I use combinations?

Use combinations when you only care which items are chosen, not the order they appear in.

Question

When should I use permutations?

Use permutations when the arrangement matters, such as ranking winners or assigning positions.

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