## Combinations

A combination is an unordered collection of unique elements (an ordered collection is called a permutation.). Given the set,

*S*, of all possible unique elements, a combination is a subset of the elements of

*S*. The order of the elements in a combination is not important (i.e., two lists with the same elements in different orders are considered to be the same combination). Addtionally, the elements cannot be repeated in a combination (i.e., every element appears once); this is often referred to as "without replacement/repetition".

Thus, for integers n and r with n ≥ r ≥ 0:

Example:

Solution: