Combinations Calculator
Count how many different groups of k items you can pick from n items when order does not matter, often written nCr or n choose k. It is used for lottery odds, team picks, card hands and probability homework.
- Runs in your browser
- Free, no account needed
- Copy or download the result
Result
Example
10
120
How to use the combinations calculator
- Type the total number of distinct items, n, in the box. Use a whole number from 0 through 10,000.
- Set Items to choose, k (0 to 1,000). It cannot be larger than n.
- Press Run to see the number of combinations.
- Press Copy result or Download to keep the full number.
How it works
Combinations = n! / (k! x (n - k)!), where n! means n x (n - 1) x ... x 1. Choosing 3 from 10 gives 120.
Items are chosen without replacement, so each one is used at most once, and the order of picks does not matter.
Results are exact whole numbers using big integer math, even when they run to hundreds of digits.
n must be from 0 to 10,000 and k from 0 to 1,000. Negative values, decimals and k larger than n are rejected.
Choosing 0 items gives 1, because there is exactly one empty group.
Everything runs in your browser. Your input is not uploaded or stored.
Questions and answers
What is the formula for combinations?
C(n, k) = n! / (k! (n - k)!). For 10 choose 3, that is 3,628,800 / (6 x 5,040) = 120.
What is the difference between combinations and permutations?
Combinations ignore order, so picking A then B is the same group as B then A. Permutations count each order separately, so they are never smaller than combinations.
How many combinations are there in a 6 from 49 lottery?
49 choose 6 is 13,983,816, so one ticket has a 1 in 13,983,816 chance of matching all six numbers.
Does this allow repeated items?
No. It counts selections without replacement, where each item can be picked only once.