Permutation and Combination Calculator
Last updated: November 5, 2026
Calculate combinations and permutations for choosing r items from n items.
Combinations nCr
—
- Permutations nPr: —
- r factorial: —
- Probability of one specific combination: —
On this page
Quick summary: Calculate combinations and permutations for choosing r items from n items.
Read the complete guide
Updated reference sections in this guide are in English.
What this calculator estimates
Calculate combinations and permutations for choosing r items from n items.
How to use it
Enter Total items n; Selected items r. Select Calculate to update the results.
How the calculation works
Combinations divide n factorial by r factorial and n minus r factorial; permutations omit the division by r factorial.
Worked example: starting scenario
| Total items n | 10 |
|---|---|
| Selected items r | 3 |
| Combinations nCr | 120 |
|---|---|
| Permutations nPr | 720 |
| r factorial | 6 |
| Probability of one specific combination | 0.008333333333 |
Important limitations
Inputs must be whole numbers with r no greater than n, and n is limited to 170.
Whether order matters changes the count
Selecting 2 people from 5 gives C(5,2) = 10 unordered groups. Assigning two distinct roles gives P(5,2) = 20 ordered assignments. This model samples without replacement and requires whole values with 0 ≤ r ≤ n ≤ 170. The reciprocal-combination probability assumes every unordered group is equally likely; it does not describe arbitrary weighted selection.