Geometry

Question Analysis
This question involves a combination problem with a “at least” condition.
The main focus is on breaking down the problem into different cases based on the number of seniors in the committee and then using the combination formula and the addition principle to find the total number of combinations.

Key Concept Explanation
The combination formula is used for each case.
The addition principle states that if there are multiple non - overlapping ways to achieve a result, the total number of ways is the sum of the number of ways for each case.

Step - by - Step Solution
Case 1: 2 seniors and 3 juniors
Number of ways to choose 2 seniors out of 8:
Number of ways to choose 3 juniors out of 12:
Total ways for this case:

Case 2: 3 seniors and 2 juniors
Number of ways to choose 3 seniors out of 8:
Number of ways to choose 2 juniors out of 12:
Total ways for this case:

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