Combinations count the ways to choose items when order does not matter, like picking a team. Permutations count the ways when order does matter, like awarding gold, silver and bronze.
How to use this calculator
Enter n, the number of items in the set, and r, how many you choose. The calculator returns both nCr and nPr.
The formulas
Combinations: nCr = n! / (r! x (n - r)!). Permutations: nPr = n! / (n - r)!. A permutation count is always r! times larger than the combination count.
Worked example
Choosing 3 people from 10 gives 10C3 = 120 possible teams. If the three roles are different (president, secretary, treasurer), there are 10P3 = 720 ways to fill them, which is 120 x 6.
Frequently asked questions
When do I use combinations versus permutations? Ask whether swapping two chosen items gives a different result. If it does, use permutations.
How large can n be? Up to 170, after which factorials exceed what a standard number can hold.