*n*elements, any subset of E that includes

*k*elements.

In a combination, the order of elements is not involved.

**combination without repetition or without reduction**

Synonym of combination.**combination with repetition or with reduction**

Combination of elements in a set E in which the repetitions (or reductions) are allowed or where the order of elements chosen is not involved.

### Formula

The number of combinations of *n* elements of a set E taken *k* at a time is given by this relation:

### Examples

Consider the set E = {2, 4, 6, 8}.

Here are a few examples of combinations of elements of E taken 2 at a time:

{2, 4}, {2, 8}, {6, 8}, {4, 8}.

Here are a few examples of combinations of elements of E taken 2 at a time with repetitions:

{2, 4}, {2, 2}, {6, 8}, {4, 4}.

The subsets {2, 8} and {8, 2} represent the same combination.

To calculate the number of combinations of elements of E taken 2 at a time, we use the formula:

\(C_{4}^{2}=\dfrac {4!} {2!\left( 4−2\right) !}\space =\space \dfrac{24}{2×2}\space =\space 6\)

If there is repetition or reduction, we use this formula:

\(K_{4}^{2}=\dfrac {(4+2−1)!} {2!\left( 4−1\right) !}\space =\space \dfrac{120}{12}\space =\space 10\)