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To solve this, let's define:

- \( M \): the set of students enrolled in Mathematics.
- \( E \): the set of students enrolled in Economics.
- \( S \): the set of students enrolled in Sociology.

We are given:
- Total students, \( |M \cup E \cup S| = 100 \).
- \( |M| = 47 \), \( |E| = 47 \), \( |S| = 57 \).
- Students enrolled in all three courses, \( |M \cap E \cap S| = 7 \).

To find the number of students enrolled in exactly one course, we can use the principle of inclusion-exclusion.

### Step 1: Set up the Inclusion-Exclusion Formula

The formula for three sets is:
\[
|M \cup E \cup S| = |M| + |E| + |S| - |M \cap E| - |E \cap S| - |S \cap M| + |M \cap E \cap S|
\]

### Step 2: Substitute the Known Values

Substitute the values into the formula:
\[
100 = 47 + 47 + 57 - |M \cap E| - |E \cap S| - |S \cap M| + 7
\]
\[
100 = 158 - (|M \cap E| + |E \cap S| + |S \cap M|)
\]
\[
|M \cap E| + |E \cap S| + |S \cap M| = 58
\]

### Step 3: Calculate Students in Exactly One Course

Let’s define:
- Students in exactly one course in Mathematics = \( |M| - (|M \cap E| + |M \cap S| - |M \cap E \cap S|) \)
- Similarly for Economics and Sociology.

After all

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?

Learn how to determine the number of students enrolled in exactly one elective course among Mathematics, Economics, and Sociology, using the Inclusion-Exclusion Principle. Given the enrollments and overlap data, find the answer in a structured approach.

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