OmniCalcsAdvertisement
Combinations & Permutations Calculator
How many ways can you choose or arrange items? Get nCr and nPr in one click.
Advertisement
How to Use This Calculator
Choosing 3 winners from 10 people where order matters gives 10P3 = 720 outcomes. If any 3-person group wins regardless of order, it's 10C3 = 120.
- Lottery-style draws โ combinations (order irrelevant).
- Passwords, sequences, lineups โ permutations (order matters).
Frequently Asked Questions
What's the difference between nCr and nPr?
nCr counts ways to choose a group (ABC = ACB). nPr counts ways to arrange a group (ABC โ ACB). Permutations are always larger.
Why is nPr always bigger than nCr?
Because every combination of r items can be arranged in r! different orders, so nPr = nCr ร r!.
What if r is greater than n?
Both answers are 0 โ you can't choose or arrange more items than exist.
What is 0! ?
By definition, 0! = 1. This keeps the formulas consistent, e.g. nCn = 1.
Practical Example
Choosing 3 winners from 10 people:
- If order matters (1st, 2nd, 3rd place) โ 10P3 = 10ร9ร8 = 720
- If order doesn't matter (any 3-person team) โ 10C3 = 120
- Each combination can be ordered 3! = 6 ways, so 120 ร 6 = 720.
What Your Results Mean
- nCr (combinations) โ the number of distinct groups you can pick, ignoring arrangement.
- nPr (permutations) โ the number of distinct ordered arrangements.
- n! โ the total arrangements of all n items, used inside both formulas.
Trusted Sources
Advertisement