The correct answer is:

A. Permutations should be used because no student may be selected more than once and the order matters.

Explanation:

In this scenario, the order of selection does matter because each student is being assigned a distinct role in the play. Thus, assigning Student A to Role 1 and Student B to Role 2 is different from assigning Student A to Role 2 and Student B to Role 1. This indicates that we need to consider the order of selection, which aligns with the concept of permutations.

Additionally:

• Permutations apply when order is important and each selection is unique, which matches this problem's requirements.
• Combinations would apply if the order did not matter.
• Arrangements with repetition would apply if students could be selected more than once, which is not the case here.

Would you like more details on solving permutation problems or have any questions?

Here are 5 related questions:

1. How many total permutations are possible when assigning roles to 4 students out of a group of 27?
2. What changes if the roles are no longer distinct, and we are only picking 4 students without regard to role?
3. Can we solve similar problems using combinations, and if so, when would combinations be appropriate?
4. How does the permutation formula change when repetition is allowed?
5. How can we visualize permutations versus combinations in a simpler example, such as choosing 2 students from a group of 3?

Tip: When deciding between permutations and combinations, remember that order matters in permutations but not in combinations.