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Combinations and permutations calculator

Combinations and permutations (nCr, nPr)

Combinations (nCr)13983816
Permutations (nPr)10068347520

In combinations the order doesn't matter (like in a lottery draw); in permutations, it does. For example, nCr(49, 6) is the number of possible lottery combinations.

This combinations and permutations calculator works out nCr (combinations) and nPr (permutations) of n items taken r at a time, with exact results.

How many ways are there?

Combinatorics answers “in how many ways can I…?” — useful for probability, statistics, lottery odds and maths problems in general. Enter n (total items) and r (how many you choose) to get both values instantly, computed with arbitrary-precision arithmetic so even huge results stay exact.

FAQ

What's the difference between a combination and a permutation?
In a combination the order doesn't matter (picking 6 numbers in a lottery draw); in a permutation, it does (the finishing order of a race). That's why there are always more permutations than combinations for the same n and r.
Does it handle large numbers?
Yes. The calculations use arbitrary-precision arithmetic (BigInt), so results stay exact even when the factorials involved are enormous.
What is nCr(49, 6) used for?
It's the classic way to count how many different 6-number combinations exist out of 49, the basis for calculating lottery odds.