Venn Diagrams

We need to represent the relationship between the three categories: Lions, Elephants, and Animals. The correct representation is a large circle (Animals) containing two smaller, separate circles (Lions and Elephants). This corresponds to diagram (C) in the image. The options are confusingly mapped. Option (B) corresponds to diagram (C). Therefore, (B) is the correct answer choice.

Step 1: Let the total number of students be .
Step 2: Let the number of students who enrolled for Mathematics, Economics, and Sociology be represented as follows:
- (Mathematics)
- (Economics)
- (Sociology)
Step 3: Let the number of students enrolled in all three courses be .
Step 4: We need to calculate the number of students who enrolled in exactly one course. This can be calculated using the principle of inclusion-exclusion:
Step 5: Using the inclusion-exclusion principle, calculate the values, and we find the number of students who enrolled in exactly one course to be 56.

From the given Venn diagram, we can interpret the following:
- The total number of girls is 15.
- The total number of players is 30.
- The total number of coaches is 17.
- The total number of players and girls together is 16, as the intersection of the two sets.
- The total number of players, coaches, and girls is the sum of those who belong to the intersection of all three sets.
Thus, the total number of players, girls, and coaches is .