Variations without Repetition Calculator

Calculation of possible variations without repetition


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.


Calculate variations

 Input
Total quantity n
Selection k
  Result

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:

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

Other Combinatorics Functions

Combinations with Repetition
Combinations without Repetition
Permutations
Rule of Product
Variations with Repetition
Variations without Repetition
Activity Selection Problem

Is this page helpful?            
Thank you for your feedback!

Sorry about that

How can we improve it?