Question

A university is offering elective courses in Mathematics, Economics, and Sociology. Each of its 100 undergraduate students has to opt for at least one of these electives. Course enrollment data showed that 47 students enrolled for Mathematics, 47 students enrolled for Economics, and 57 students enrolled for Sociology. If 7 students enrolled for all three courses, how many students enrolled for exactly one course?

• A. 60
• B. 56
• C. 58
• D. Can't say

Hint:

To calculate students enrolled in exactly one course, use the principle of inclusion-exclusion to subtract those enrolled in multiple courses.

Answer 1

The Correct Option is B

Step 1: Let the total number of students be \( n = 100 \).
Step 2: Let the number of students who enrolled for Mathematics, Economics, and Sociology be represented as follows:
- \( M = 47 \) (Mathematics)
- \( E = 47 \) (Economics)
- \( S = 57 \) (Sociology)
Step 3: Let the number of students enrolled in all three courses be \( x = 7 \).
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:
\[ \text{Exactly one course} = M + E + S - 2 \times (\text{students enrolled in two courses}) - 3 \times (\text{students enrolled in all three courses}) \] 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.