Permutations and combinations count the number of ways to select items from a set. Permutations care about order (P(n,r) = n!/(n-r)!), while combinations don't (C(n,r) = n!/(r!(n-r)!)). The key question: does the arrangement order matter?
How to Use
Enter n and r:
- n: Total number of items
- r: Number to select
- Results: Both nPr and nCr calculated
The Formulas
- Permutation: P(n,r) = n! / (n−r)!
- Combination: C(n,r) = n! / (r! × (n−r)!)
- Relationship: P(n,r) = C(n,r) × r!
When to Use Each
- Permutation: Ranking, passwords, seating arrangements
- Combination: Lottery, committees, handshakes, teams
Step-by-Step Instructions
- 1Enter the total items (n).
- 2Enter the selection size (r).
- 3View permutation and combination results.
- 4Check the step-by-step factorial breakdown.
- 5Compare nPr vs nCr.