Combinations

Given a set of n elements, combinations are different groups formed by the k elements of a subset such that:

The order of the elements does not matter.

The elements are not repeated.

Combinations

Also, the combinations can be calculated by means of factorials:

Combinations and Factorials

The combinations can also be denoted as a combinatorial number: Combinatorial Number.

Examples

1. Calculate C(10,4).

Combination Example

Combination Solution

2. A student council committee of three students has to be selected out of a class of 35 students. How many different committees can be formed?

The order of the elements does not matter.

The elements cannot be repeated.

Combination Solution