Possible Combinations Calculator
Enter the number of distinct items and selection size to see counts for four scenarios: combinations/permutations with and without repetition.
| Scenario | Count | Formula |
|---|---|---|
| Combination (no repetition) | 210 | C(n, k) = n! / (k!(n − k)!) |
| Combination with repetition | 715 | C(n + k − 1, k) |
| Permutation (no repetition) | 5,040 | P(n, k) = n! / (n − k)! |
| Permutation with repetition | 10,000 | nᵏ |
How to Use This Calculator
- Enter n (total distinct elements).
- Enter k (number of selections/positions).
- Review counts for combinations and permutations with and without repetition.
- Apply the results to counting, probability, or combinatorial problems.
Formula
Combination: C(n, k) = n! / (k!(n − k)!)
Combination with repetition: C(n + k − 1, k)
Permutation: P(n, k) = n! / (n − k)!
Permutation with repetition: nᵏ
Full Description
Combinatorics provides formulas for counting selections and arrangements. This calculator collects the four primary scenarios—combinations/permutations with and without repetition—so you can compare results and pick the formula relevant to your problem.
Frequently Asked Questions
What if k > n?
Combinations without repetition become zero because you can’t choose more items than available. With repetition, k can exceed n.
Why does permutation with repetition use nᵏ?
Each position can be filled by any of the n options independently, leading to n choices per position, repeated k times.
Do negative inputs work?
No. n and k must be non-negative integers. Inputs are rounded to appropriate values.
When should I use combinations with repetition?
Use it when selections allow repeated items but order does not matter (stars-and-bars problems).