Geometry

Question Analysis
This question requires analyzing a Venn Diagram to calculate the probability of a compound event where students participate in exactly two clubs.
The main focus is on correctly identifying and summing up the relevant regions in the Venn Diagram and then calculating the probability.

Key Concept Explanation
We need to find the sum of the regions that represent students participating in exactly two clubs (i.e., the intersections of pairs of clubs without including the intersection of all three clubs).
The probability is then this sum divided by the total number of students in the class (the sum of all regions in the Venn Diagram).

Step - by - Step Solution
Calculate the number of students who participate in exactly two clubs. The regions are A and M only (6 students), A and S only (4 students), and M and S only (5 students). So the number of favorable outcomes is .
Calculate the total number of students. Add up all the numbers in the Venn Diagram:

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