Combinations and Permutations Calculator
Calculate combinations nCr and permutations nPr for probability and counting problems
About this calculator
This combinations and permutations calculator helps you solve complex counting problems in probability, statistics, and mathematics. It instantly computes nCr (combinations) when order doesn't matter, like selecting team members, and nPr (permutations) when order is important, like arranging winners. Essential for students, researchers, and professionals working with probability calculations, lottery odds, statistical analysis, and combinatorial mathematics.
How to use
Enter your total number of items (n) and the number you're selecting (r). Choose whether you need combinations (nCr) for selections where order doesn't matter, or permutations (nPr) where order is important. Click calculate to get your result instantly with the mathematical formula shown.
Frequently asked questions
What's the difference between combinations and permutations?
Combinations (nCr) count selections where order doesn't matter, like choosing pizza toppings. Permutations (nPr) count arrangements where order matters, like race finishing positions.
When would I use nCr vs nPr?
Use nCr for selecting groups, teams, or subsets. Use nPr for arranging items in sequence, passwords, or when position matters in your selection.
What are the mathematical formulas used?
Combinations: nCr = n!/(r!(n-r)!). Permutations: nPr = n!/(n-r)!. Both use factorials where n! means n×(n-1)×(n-2)×...×1.