Frequently Asked Questions
When do I use P(n,r) vs C(n,r)?
Use P(n,r) when order matters (race finishes, passwords). Use C(n,r) when it doesn't (lottery picks, committee selections). C is always smaller than P.
What is the formula for combinations?
C(n,r) = n! / (r! × (n−r)!). It counts the number of unordered subsets of size r from n items.
Why is 0! defined as 1?
For consistency with the formulas: C(n,0) = 1 only works if 0! = 1. There is exactly one way to choose nothing.
How big can these numbers get?
Very fast. C(52,5) = 2,598,960 poker hands. P(10,10) = 10! = 3,628,800 orderings. Factorial growth quickly exceeds calculator limits.
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Important Disclaimer: Estimates for informational purposes only.
This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.