How to use it
- Enter your items, separated by commas, spaces or new lines.
- Set k, how many items to choose.
- Choose whether an item may repeat.
- Read the count and copy or download the list.
What a combination is
A combination is a selection where order doesn't matter: picking A, B, C is the same as picking C, A, B. The number of ways to choose k items from n different items is
C(n, k) = n! / (k! · (n − k)!), also written nCr or "n choose k".
Example: choosing 3 toppings from 5 (A, B, C, D, E):
C(5, 3) = 5! / (3! · 2!) = 120 / (6 · 2) = 10
ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, CDE.
If order does matter (ABC and CBA are different), you want permutations instead: see the permutation generator.
Combinations with repetition
Turn on With repetition when the same item can be chosen more than once, like scoops of ice cream where you can take two of the same flavor. The count becomes
C(n + k − 1, k)
Choosing 3 scoops from 5 flavors with repetition allowed: C(7, 3) = 35 combinations, including AAA, AAB and so on.
| n items | k chosen | Without repetition | With repetition |
|---|---|---|---|
| 5 | 2 | 10 | 15 |
| 5 | 3 | 10 | 35 |
| 10 | 3 | 120 | 220 |
| 52 | 5 | 2,598,960 | 3,819,816 |
The 2,598,960 is the classic number of different five-card poker hands from a 52-card deck.
Calculating nCr by hand
You rarely need to compute full factorials. Cancel first:
C(10, 3) = 10! / (3! · 7!) = (10 · 9 · 8) / (3 · 2 · 1) = 720 / 6 = 120
In general, multiply k numbers counting down from n, then divide by k!. Two shortcuts help too: C(n, k) = C(n, n − k), so choosing 8 of 10 is the same as choosing which 2 to leave out (45), and C(n, 1) = n, C(n, n) = 1.
How the tool works
- Items: type them separated by commas, spaces or new lines; auto-detect figures out which. You can also treat every character as an item, so ABCDE means five items. Duplicate items are merged. Up to 200 distinct items.
- k: 1 to 50 (and at most n without repetition).
- Output: each combination on its own line, items joined by a comma, space, nothing, hyphen, pipe or tab. Numbered adds 1., 2., 3. in front.
The count is calculated exactly, however large it is. The list itself is limited to the first 50,000 combinations, in lexicographic order (following the order of your items), so your browser stays responsive. All work happens locally.
Lottery odds and other uses
Combinations explain lottery odds. In Powerball you pick 5 white balls from 69, and the order doesn't matter, so there are C(69, 5) = 11,238,513 possible sets. Multiplied by the 26 possible red Powerballs, that's 292,201,338 combinations, the familiar 1 in 292.2 million jackpot odds.
Other everyday uses:
- Teams and pairings: how many ways to pick a committee of 4 from 12 people (495), or every pair in a group for a round-robin.
- Menus and bundles: all 2-item side combinations.
- Testing: every pair of settings to test together.
- Homework: check nCr answers and see the full list.
For every combination of words across different lists (one from each list), use the keyword combiner instead.
Frequently asked questions
What is the formula for combinations?
C(n, k) = n! / (k! · (n − k)!). For example, C(5, 3) = 10.
What is the difference between combinations and permutations?
In combinations order doesn't matter (ABC = CBA). In permutations it does, so there are more of them.
How many combinations of 3 are there from 10 items?
120 without repetition, or 220 if items can repeat.
Can it list all combinations?
Yes, up to 50,000 at a time. The total count is always shown exactly.
What does “with repetition” mean?
The same item can be picked more than once, such as AAB. The count is C(n + k − 1, k).
Last updated: November 12, 2026