Loading calculator...
Loading calculator...
Calculate permutations P(n,r) and combinations C(n,r) for selecting r items from a set of n items.
Permutations and Combinations:
Permutation P(n,r) = n! / (n-r)! — order matters
Combination C(n,r) = n! / (r! x (n-r)!) — order does not matter
C(n,r) is also called n-choose-r or the binomial coefficient.
A permutation is an arrangement of items where order matters. P(n,r) counts how many ways to arrange r items chosen from n, when the order of selection matters.
A combination is a selection where order does not matter. C(n,r) counts how many ways to choose r items from n, when the order is irrelevant.
In permutations, different orderings count as separate outcomes (ABC ≠ BCA). In combinations, only the set of selected items matters (ABC = BCA). So P(n,r) >= C(n,r) always.
The factorial of n (written n!) is the product of all positive integers from 1 to n. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120. By definition, 0! = 1.
No. You cannot choose or arrange more items than are available. If r > n, the result is 0 by convention.