A college offers 7 courses in the morning and 5 in the evening. Find the number of ways a student can select exactly one course, either in the morning or in the evening.

Answer

To solve the problem of selecting exactly one course from either the morning or evening offerings at a college, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Number of Courses**:
- The college offers 7 courses in the morning.
- The college offers 5 courses in the evening.

2. **Understand the Selection Criteria**:
- A student can select exactly one course, which can either be from the morning or from the evening.

3. **Calculate the Number of Ways to Select a Course**:
- The number of ways to select one course from the morning courses is given by \(7C1\).
- The number of ways to select one course from the evening courses is given by \(5C1\).

4. **Use the Combination Formula**:
- The combination formula \(nCr\) represents the number of ways to choose \(r\) items from \(n\) items without regard to the order of selection.
- Here, \(nC1 = n\) because choosing 1 item from \(n\) can be done in \(n\) ways.
- Therefore, \(7C1 = 7\) and \(5C1 = 5\).

5. **Add the Two Results**:
- Since the student can choose either from the morning or the evening, we add the two results:
\[ \text{Total ways} = 7C1 + 5C1 = 7 + 5 = 12 \]

6. **Conclusion**:
- The total number of ways a student can select exactly one course, either in the morning or in the evening, is **12**.