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