How to Use the Combinations and Permutations Calculator
Combinatorics is the mathematics of counting. Use this to calculate exactly how many ways you can select or arrange items from a set.
Step-by-Step Instructions
- 1 Enter the total number of items (n).
- 2 Enter the number of items to choose (r).
- 3 Click Calculate to see both combinations (nCr) and permutations (nPr).
Understanding the Inputs
n (total)
The total number of items in your set. For example, 52 for a deck of cards, 10 for a group of people, or 20 for a pool of candidates.
How to find it: This is the size of your complete set. In a lottery where you pick 6 numbers from 49, n=49.
Why it matters: The total set size determines the maximum number of possible selections. A larger n means exponentially more combinations.
Type: number · Default: 0
r (choose)
The number of items you are selecting or arranging. For example, drawing 5 cards from a deck means r=5. Choosing 3 winners from a group means r=3.
How to find it: This is the size of your subset. R must be less than or equal to n.
Why it matters: The selection size dramatically affects the count. C(10,2)=45 but C(10,8)=45 (same, symmetric). C(10,5)=252 (maximum at r=n/2).
Type: number · Default: 0
Tips & Best Practices
- ✓ Combinations are used when order does not matter (poker hands, lottery numbers).
- ✓ Permutations are used when order matters (passwords, race results, seating arrangements).
- ✓ nCr is symmetric: nCr = nC(n-r). C(10,3) = C(10,7) = 120.
Try the Combinations and Permutations
by CalculatorPro Tools · Updated 2026-07-29