Combination Calculator
Calculate the number of combinations (nCr) — the number of ways to choose r items from a set of n items, where order doesn't matter.
- Free to use
- Accurate results
- No registration required
- Works on all devices
Enter n (total items) and r (items chosen) to calculate the number of combinations (nCr) — unordered selections of r items from a set of n.
Must be less than or equal to n.
Your result
10
Number of combinations (nCr)
Number of permutations (nPr)60
AI explanation
Formula
nCr = n! / (r! × (n − r)!)Worked example
Choosing 3 items from 5 (order doesn't matter)
| Field | Value |
|---|---|
| Total items (n) | 5 |
| Items chosen (r) | 3 |
| Number of combinations (nCr) | 10 |
| Number of permutations (nPr) | 60 |
Assumptions
- Order does not matter in a combination — choosing items A, B, C is the same combination regardless of the order they were picked in.
- r cannot be greater than n.
Frequently asked questions
What is a combination?
A combination is a selection of items where order doesn't matter — choosing items A, B, C is the same combination no matter what order you picked them in.
How many combinations are there in a lottery draw?
For a typical 6-number draw from 49 numbers, there are 49C6 = 13,983,816 possible combinations — this calculator can compute that exact figure for any n and r.
How is nCr related to nPr?
nCr = nPr / r! — a combination count is the permutation count divided by the number of ways to arrange the r chosen items among themselves, since order doesn't matter for combinations.