Combinations and Permutations
Calculate combinations (nCr) and permutations (nPr) for any values.
What Is the Combinations and Permutations?
A combinations and permutations calculator computes how many ways you can select items from a set. Combinations (nCr) count selections where order does not matter. Permutations (nPr) count selections where order matters.
The Formula
nCr = n! / (r! x (n-r)!). nPr = n! / (n-r)!.
Example
Choosing 3 committee members from 10 candidates gives 120 combinations where order does not matter. Arranging 3 books from 10 on a shelf yields 720 permutations since each position is distinct. These formulas power poker hand analysis, tournament bracket design, and lottery probability calculations.
Common Uses
Lottery odds, card game probabilities, scheduling, tournament brackets, password cracking estimation.
Frequently Asked Questions
How does the Combinations and Permutations work? ▼
Enter your numbers into the input fields and the calculator processes them instantly. Each input has a label explaining what to enter. Results are displayed clearly with context to help you understand them.
Is the Combinations and Permutations free? ▼
Yes, all calculators on CalculatorPro Tools are completely free. No registration, no sign-up, and no hidden fees. Just enter your numbers and get results instantly.
Can I trust the accuracy? ▼
Yes, calculations are mathematically exact using standard formulas. We recommend verifying important results independently for critical applications.
Common Mistakes to Avoid
- ⚠ Not double-checking input values before calculating.
- ⚠ Using results for critical decisions without professional verification.
- ⚠ Applying the calculator to situations outside its intended use case.