Permutation and Combination Calculator
Enter n and r to compute both permutations and combinations.
P(n,r)=n!/(n-r)! | C(n,r)=n!/(r!(n-r)!)n= Total items
r= Items chosen
Tips & Notes
- ✓C(n,r) = C(n,n-r).
- ✓0! = 1 by definition.
- ✓Combinations <= permutations always.
- ✓Results grow astronomically for large n.
Common Mistakes
- ✗Using permutations when combinations needed.
- ✗r exceeding n.
- ✗Not simplifying factorials.
- ✗Confusing the two formulas.
Permutation and Combination Calculator Overview
What This Calculator Does
Computes nPr (ordered) and nCr (unordered) from n and r. Permutations count arrangements where order matters; combinations count selections where it does not.
Formulas
P(n,r) = n!/(n-r)! and C(n,r) = n!/(r!(n-r)!). Both require n >= r >= 0.
When to Use Each
Permutations: rankings, passwords, sequences. Combinations: committees, lottery draws, card hands. The relationship C(n,r) = P(n,r)/r! shows combinations are always fewer.
Applications
Probability calculations, lottery odds, genetic combinations, poker hands, and experimental design.
Frequently Asked Questions
Permutations when order matters, combinations when it does not.
1, by definition.
About 170 before losing precision.
The Permutation and Combination Calculator uses standard validated formulas and provides results accurate to multiple decimal places. Review the step-by-step explanation to verify each calculation.