Numbers
Combination Calculator
Used by developers, writers, and creators worldwide.
A combination calculator works out how many ways you can choose r items from a set of n when the order does not matter — the quantity written C(n, r) or "n choose r". Enter the totals and it returns the exact count using big-integer arithmetic, so large values are precise rather than rounded. Students use it to check combinatorics homework, teachers to generate examples, and anyone working with probability, lotteries, or card hands to count possibilities quickly. Combinations are everywhere odds appear — the number of possible lottery tickets, poker hands, or committees — and the formula's factorials make them awkward by hand. The result reminds you that combinations ignore order, the key distinction from permutations: choosing Alice then Bob is the same combination as Bob then Alice. Use it to verify a calculation, explore odds, or build intuition for how fast the count of possible groups grows.
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How to use
- Choose your options above
- Click Generate
- Copy your result
Detailed instructions
- Enter the total number of items, n.
- Enter how many you are choosing, r.
- Click Generate to compute C(n, r) exactly.
- Use the result to check work or compute odds.
Use Cases
- •Checking combinatorics homework answers
- •Counting possible lottery tickets or card hands
- •Computing probabilities that depend on combinations
- •Generating worked examples for a class
- •Counting how many groups can be formed from a set
Tips
- →Combinations ignore order — use permutations if order matters.
- →C(n, r) equals C(n, n−r), a handy shortcut.
- →Pair with the factorial tool to see the formula behind it.
- →Large counts are exact thanks to big-integer maths.
FAQ
what is a combination
A combination is a selection of items where order does not matter. C(n, r) counts how many distinct groups of r you can choose from n items. Choosing Alice then Bob gives the same combination as Bob then Alice.
how is it different from a permutation
Permutations count ordered arrangements, so they treat Alice-then-Bob as different from Bob-then-Alice. Combinations ignore order, so they are always fewer than or equal to the matching permutation count for the same n and r.
are the results exact for large inputs
Yes. The calculation uses big-integer arithmetic and divides as it goes to stay exact, so even large combination counts are precise to the final digit rather than rounded.