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Get NordVPN →Combination Calculator (nCr) — Choose r from n
This combination calculator computes nCr = n! / (r!·(n−r)!), the number of ways to choose r items from a set of n when order does not matter. Enter n and r (with 0 ≤ r ≤ n) to get the result instantly for combinatorics and probability problems.
Enter n and r to see the number of combinations.
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How it works
What is a combination?
A combination counts how many distinct groups of r items you can choose from n items when the order of selection does not matter. Picking {A, B} is the same as picking {B, A}.
The count is written nCr or C(n, r) and is calculated with the formula nCr = n! / (r!·(n−r)!), valid whenever 0 ≤ r ≤ n.
Combinations vs. permutations
Use a combination when order is irrelevant, such as selecting a committee or a lottery draw. Use a permutation when order matters, such as ranking finishers in a race.
Because permutations count ordered arrangements, nPr is always greater than or equal to nCr: nPr = nCr · r!.
Frequently asked questions
›What does nCr mean?
nCr is the number of combinations: how many ways you can choose r items from n when order does not matter.
›What is the formula for nCr?
nCr = n! / (r!·(n−r)!), where n! is the factorial of n. It is valid when 0 ≤ r ≤ n.
›What is the difference between a combination and a permutation?
A combination ignores order, while a permutation counts ordered arrangements. nPr = nCr · r!.
›What is nC0 or nCn?
Both equal 1. There is exactly one way to choose nothing and exactly one way to choose everything.
›Can r be greater than n?
No. The formula requires 0 ≤ r ≤ n; you cannot choose more items than are available.
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