Variations without Repetition Calculator

This function calculates the number of possible variations from a set without repetition. In the case of variations without repetition, a number k is selected from the total n, taking into account the order.

Description of variations without repetition

The Variation Without Repetition function calculates how many ways there are to order a given set of objects. When combining the variations, a number k is selected from the total n, taking into account the order.

Each object may only be selected once in the object group, i.e. without repetition. In the case of the urn model, this corresponds to a draw without replacement but with consideration of the order.

This example shows how many groups with 2 objects from the digits 1 to 3 can be formed. They are the groups (1,2), (2,1), (1,3), (3,1), (2,3) and (3,2). So six groups.

Example and formula

Four balls are to be drawn from a box with six different colored balls. The number of ways to select and order four balls is calculated using the following formula:

\(\displaystyle \frac{n!}{(n-k)!}=\frac{6!}{(6-4)!}=\frac{6!}{2!}= \frac{1·2·3·4·5·6}{1·2}=\frac{720}{2}=360 \)