Permutation & Combination Calculator
Calculate permutations, combinations, and arrangements with or without repetition. Solve combinatorial problems with detailed step-by-step explanations.
Combinatorics Calculator
Choose your calculation type and enter the parameters
Total number of items available
Number of items to select
Permutation
P(n,r) = n! / (n-r)! - Order matters, no repetition
Combinatorics Fundamentals
Permutation
Arrangement of objects where order matters. Different sequences are counted as different arrangements.
Example: ABC, ACB, BAC are all different permutations
Combination
Selection of objects where order doesn't matter. Different sequences are counted as the same group.
Example: {ABC}, {ACB}, {BAC} are all the same combination
With Repetition
Objects can be selected multiple times. The same item can appear more than once in your selection.
Example: AAA, AAB, ABB are all valid when repetition is allowed
Without Repetition
Each object can only be selected once. No item appears more than once in your selection.
Example: ABC is valid, but AAA is not allowed
When to Use Which?
Use Permutation When:
- Arranging people in a line
- Race finishing positions
- Password creation
- Seating arrangements
Use Combination When:
- Selecting team members
- Choosing pizza toppings
- Lottery number selection
- Committee formation