Permutation without Repetition Calculator

A permutation without repetition is an ordered arrangement of elements from a set where each element can be used only once. The order matters — selecting A then B is considered a different permutation from selecting B then A. This differs from combinations, where order is irrelevant.

The formula is P(n, r) = n! / (n − r)!, where n is the total number of objects in the set and r is the number of objects you are selecting. The exclamation mark denotes a factorial — for example, 5! = 5 × 4 × 3 × 2 × 1 = 120.

If you are arranging all 5 numbers (r = 5), then P(5, 5) = 5! / (5−5)! = 120 / 1 = 120. If you are only choosing 3 from those 5, P(5, 3) = 5! / 2! = 120 / 2 = 60 permutations.

Use the formula P(11, r) = 11! / (11 − r)!. For example, choosing 4 from 11 gives P(11, 4) = 11! / 7! = 7920. Simply enter n = 11 and r = 4 into this calculator to get the result instantly.

With repetition, you can reuse the same element multiple times, giving nʳ arrangements. Without repetition, each element may appear at most once in an arrangement, giving n! / (n−r)! arrangements. Without repetition always yields fewer or equal results compared to with repetition.

No. If r is greater than n, there are not enough distinct elements to fill all positions without reusing any, so the result is undefined (or zero valid permutations). Make sure r ≤ n when using this calculator.

In a permutation, the order of selection matters — choosing {A, B} is different from {B, A}. In a combination, order does not matter — {A, B} and {B, A} count as the same selection. Permutations always give a larger or equal count compared to combinations for the same n and r.

Factorials grow extremely fast. 170! is approximately 7.26 × 10³⁰⁶, which is near the upper limit of standard floating-point number representation in most programming environments. Values of n beyond 170 would produce results too large to represent accurately.