Arrangement Calculator (A _n,k)

What is Simple Arrangement?

Arrangement is a content studied in combinatorics, it describes the idea that a number n of elements can be arranged and rearranged in several different ways without repetitions between the ordered elements.

Use our arrangement calculator below. Enter values between 0 and 150 for n and k (remember: n >= k):

Arrangement Formula

The array formula is represented by:

A_{n, k} = n! (n - k)!   ${\displaystyle \frac{}{}}$ $\dfrac {6!}{3!} =$ /

How to calculate Arrangement

To calculate the arrangement, it will be necessary to divide the factorial of elements(n) by the factorial obtained by subtracting the number of elements(n) minus the size of the grouping(k). For factorial division, note that there are rules! See the following example of the array calculation:

A_{5, 3} = 5! (5 - 3)!   ${\displaystyle \frac{}{}}$ $\dfrac {6!}{3!} =$ = 5! 2! ${\displaystyle \frac{}{}}$ $\dfrac {6!}{3!} =$ = 120 2   ${\displaystyle \frac{}{}}$ $\dfrac {6!}{3!} =$ = 60

Difference between Arrangement and Simple Combination

Arrangement and combination are not the same thing, to be able to differentiate, just pay attention to whether the grouping of elements depends on orders, if yes, it is an arrangement, if not, you must calculate a combination.