Let's break down the problem:

1. We have a group $N = \{ \text{Anthony, Bruce, Cindy, Douglas, Elaine} \}$.
2. Cindy and Elaine are seniors, while Anthony, Bruce, and Douglas are juniors.
3. We need to select a president, secretary, and treasurer such that:
   • The president must be a junior.
   • The secretary and treasurer must be seniors.
4. Each person can only hold one office.

Step-by-Step Solution

1. Select the President (must be a junior):

   • Eligible choices for president: Anthony, Bruce, Douglas (3 juniors).

2. Select the Secretary (must be a senior):

   • Eligible choices for secretary: Cindy, Elaine (2 seniors).

3. Select the Treasurer (must be a senior and different from the Secretary):

   • If Cindy is chosen as Secretary, Elaine must be the Treasurer.
   • If Elaine is chosen as Secretary, Cindy must be the Treasurer.
   • There are 2 ways to assign the Secretary and Treasurer.

Calculate the Total Number of Ways

Since there are 3 choices for President and 2 pairings of Secretary and Treasurer for each President, the total number of ways to select the positions is: $3 \times 2 = 6$

Verification of the Answer Choices

From the question, we need to match this number with one of the given options:

• Option A: Lists CEA, ECA, BED, CED, BCE. (Not exactly 6)
• Option B: Lists ACE, CED, BEC, CEA, BCE. (Likely 5)
• Option C: Lists ACE, AEC, BCE, BEC, DCE, DEC. (Looks like 6)
• Option D: Lists CED, BEC, CEA, ACE. (Only 4)

Conclusion

Since we computed that there are 6 possible ways, Option C seems to correctly represent the combinations of President, Secretary, and Treasurer based on the constraints.

Would you like a more detailed breakdown of each step? Here are some related questions to consider:

1. How can we generalize this selection process for different groups?
2. What would change if we added more juniors or seniors?
3. How would the answer change if any office could be held by either a junior or a senior?
4. What if Cindy and Elaine were not both required to be in different roles?
5. How can combinations and permutations help in solving such selection problems?

Tip: When selecting groups for specific roles with constraints, always identify eligible members first, then multiply the possibilities to find the total.