Permutations and combinations both count arrangements, but permutations care about order while combinations do not.
Permutations (nPr)
nPr = n! / (n-r)!. Choosing a president and vice-president from 10 people: 10P2 = 90. Use the Permutation Calculator.
Combinations (nCr)
nCr = n! / (r!(n-r)!). Choosing any 2 people from 10: 10C2 = 45. See the Combination Calculator.
When to Use Which
Order matters? Permutation. Order irrelevant? Combination.
Going Deeper
When order matters and when it doesn't - nPr vs nCr explained. This guide connects theory to practice — use the related calculators linked at the bottom to verify each example with your own numbers.
Practical Tips
- Write down given values and unknowns before opening the calculator.
- Check units and rounding rules appropriate to your context (class, lab, or business).
- Compare manual working with the calculator result to build confidence.
Common Mistakes to Avoid
- Rushing inputs without reading field labels carefully.
- Confusing similar formulas that use different variables or units.
- Reporting results with more precision than your inputs justify.
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