What is the difference between a permutation and a combination?

The distinction between permutations and combinations primarily lies in how order impacts the selection of elements. In permutations, the arrangement of the selected items is critical. Therefore, different arrangements of the same items are considered distinct. For example, the arrangements "ABC" and "ACB" are viewed as different permutations.

This understanding helps to clarify why the choice indicating that arrangement matters in permutations is correct. When working with permutations, if you have a set of items, every unique ordering of those items represents a separate permutation.

On the other hand, combinations focus on the selection of items without regard for order. Different arrangements of the same items do not change the outcome in combinations; hence "ABC" and "ACB" would count as the same combination. This underscores the significance of order in permutations but not in combinations. The concept of allowing repetitions or distinguishing between selection methods does not pertain to this key difference, which is the basis for correctly identifying that arrangements matter in permutations.