Combinations, variations and permutations
Calculate how many ways you can choose k elements out of n. With order taken into account or without it.
How do I use this page?
- Fill in the fields in the form above — the result recomputes at once, with no page reload.
- Under the result you will find the interpretation scale, if the calculator has one: it says which range your value fell into.
- The formula we use is shown lower on this page — you can check the arithmetic yourself.
- To compute the same for another game or variant, change it in the select field — prices and pools update automatically.
Further reading
Theory — what is the difference between combinations, variations and permutations?
Combinatorics answers one question: in how many ways something can be arranged or chosen. The difference between a combination and a variation comes down entirely to whether the order of elements matters. When drawing six numbers in a lottery, order does not matter, so the number of possible sets is a combination rather than a variation. Out of forty-nine numbers, exactly 13,983,816 such sets can be formed.
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Frequently asked questions
How many combinations are there of six numbers out of forty-nine?
What's the difference between a combination and a variation?
How many bets does a full system of 8 numbers have in Lotto?
Why doesn't the calculator accept n greater than 170?
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