Online Tool Store
Combination Calculator
Calculate nCr combinations from a set size and selection count, with factorial steps and a permutation comparison.
🔒 This tool runs entirely in your browser. Your files are never uploaded to a server.
Calculate combinations
Enter whole numbers where n is the total items and r is how many are chosen.
Example shown: choose 4 items from a group of 12.
Combinations
There are 495 ways to choose 4 items from 12 when order does not matter.
Notation
Permutations
r factorial
Formula
12! / (4! x (12 - 4)!) = 495
Combinations divide permutations by 4! because every selected group can be ordered 24 different ways.
How it works
- Enter n, the total number of items in the set.
- Enter r, the number of items you want to choose.
- Read the combination count, matching nCr notation, permutation comparison, and formula.
The combination formula
The calculator uses nCr = n! / (r! x (n - r)!). For 12C4, that means 12! / (4! x 8!) = 495 possible groups.
FAQ
What does nCr mean?
nCr is the number of ways to choose r items from n total items when order does not matter. It is also called a binomial coefficient.
How is this different from permutations?
Permutations count different orders as separate outcomes. Combinations count each selected group once, so ABC and CBA are the same combination.
Can r be larger than n?
No. You cannot choose more items than the total available set. The calculator shows an error if r is greater than n.
Are decimal or negative values allowed?
No. Combinations are defined here for whole-number counts: n and r must be zero or positive integers.
Is anything uploaded?
No. The arithmetic runs entirely in your browser, and the values you enter are not sent to a server.
How we compare
| Feature | Online Tool Store | Basic calculators | Spreadsheet formulas |
|---|---|---|---|
| Live nCr result | Yes | Usually | Formula required |
| Formula shown beside the answer | Yes | Sometimes | No explanation |
| Permutation comparison | Yes | Often separate | Separate formula |
| Account required | No | No | No |
Choose this calculator when you want the answer and the reasoning together: it keeps nCr notation, factorial formula, and order-sensitive permutation comparison in one browser-only workspace.