Permutation & Combination Calculator
Calculate permutations (nPr) and combinations (nCr) for any values of n and r with detailed explanations.
Calculator
Results
Enter values for n and r to see results
How It Works
Permutations (nPr)
Permutations count the number of ways to arrange r items from n total items where order matters.
Formula: nPr = n! / (n-r)!
Example: Arranging 3 people from 5 people in a line = 5P3 = 60 ways
Combinations (nCr)
Combinations count the number of ways to choose r items from n total items where order doesn't matter.
Formula: nCr = n! / (r! × (n-r)!)
Example: Choosing 3 people from 5 people for a team = 5C3 = 10 ways
Common Examples
When to Use Permutations:
- • Arranging people in a line
- • Password combinations with order
- • Race finishing positions
- • Seating arrangements
When to Use Combinations:
- • Selecting team members
- • Choosing lottery numbers
- • Selecting committee members
- • Choosing pizza toppings