To determine which of the following options is NOT a requirement for the Combinations Rule, let's go through each option and see if it aligns with the conditions required for using the combination formula:
A. That order is not taken into account (consider rearrangements of the same items to be the same).
- This is indeed a requirement for combinations. In combinations, the arrangement of items does not matter. Selecting items A, B is the same as selecting items B, A.
B. That the items are selected (without replacement).
- This is also a requirement for combinations. When selecting combinations, once an item is chosen, it cannot be chosen again.
C. That order is taken into account (consider rearrangements of the same items to be different sequences).
- This is NOT a requirement for combinations. In fact, this describes permutations, not combinations. In permutations, the order of items matters, but in combinations, it does not.
D. That there be n different items available.
- This is a requirement for combinations. The formula [tex]\({ }_n C_r\)[/tex] is used to determine the number of ways to choose r different items from n available different items.
So, the correct answer is:
C. That order is taken into account (consider rearrangements of the same items to be different sequences).
This option is NOT a requirement for the Combinations Rule because combinations deal with selections where the order does not matter.
