Combination and Permutation Calculator

Enter the total items and how many you choose to get both combinations and permutations.

Combinations versus permutations

Counting how many ways you can choose or arrange things splits into two ideas. Combinations count selections where order does not matter, like the numbers drawn in a lottery. Permutations count arrangements where order does matter, like the finishing order on a podium.

That is why permutations are always at least as many as combinations: each unselected group can be shuffled into several ordered versions. These counts power probability, statistics, and everyday questions about how many outcomes are possible.

The formula

nCr = n! / ( r! (n-r)! ); nPr = n! / (n-r)!

Worked example

Choosing 3 from 10 gives 120 combinations and 720 permutations.

How to read your result

Use combinations when order does not matter (a lottery draw) and permutations when it does (a ranked podium). Permutations are always at least as large as combinations.

Frequently asked questions

What is the difference?: Combinations ignore order; permutations count order as distinct.
When do I use each?: Combinations for selections, permutations for arrangements or rankings.
Why is nPr larger?: Because each combination can be arranged in several ordered ways.

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