How it works
- Permutations count arrangements where order matters: nPr = n! ÷ (n − r)!.
- Combinations count selections where order doesn't matter: nCr = n! ÷ (r! × (n − r)!).
- With repetition allowed, permutations are nʳ and combinations are (n + r − 1)C r.
- Answers are calculated exactly, even when they run to hundreds of digits.
Frequently asked questions
How do I know whether order matters?
If swapping two chosen items gives a different result (a PIN code, a race podium), use permutations. If it doesn't (a lottery draw, a pizza's toppings), use combinations.
How many 5-card poker hands are there?
52C5 = 2,598,960. Enter n = 52 and r = 5 to see the working.
Results are estimates for general information and are not financial, medical or professional advice.