Combinations without Repetition

Calculation of possible combinations without repetition


This function calculates the number of possible combinations from a set without repetition. When combining without repeating, a number \(k\) is selected from the total \(n\).


Calculate combinations

 Input
Total quantity n
Selection k
  Result

Description of combinations without repetition


The number of possible combinations from a set without repetition is calculated. In the case of combinations without repetition, a number \(k\) is selected from the total \(n\).

The order of the selected objects is ignored. Each object may only be selected once in the object group, i.e. without repetition. For the urn model, this corresponds to a no-replacement, no-order draw.

The formula is:

\(\displaystyle \frac{n!}{(n-k)! · k!}\)

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


Other Combinatorics Functions

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

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