A college offers 10 courses in the morning and 7 in the evening. Find the number of ways a student can select exactly one course, either in the morning or in the evening

Options

A. 10
B. 29
C. 30
D. 17

Answer

To solve the problem of how many ways a student can select exactly one course, either in the morning or in the evening, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Number of Courses:**
- The college offers **10 courses in the morning**.
- The college offers **7 courses in the evening**.

2. **Understanding the Selection:**
- The student can choose **one course from the morning** or **one course from the evening**.

3. **Calculate the Total Number of Selections:**
- The number of ways to choose one course from the morning is given by the combination formula \( nC1 \), which is simply equal to the number of courses available. Thus, for the morning:
\[ \text{Ways to choose from morning} = 10C1 = 10 \]
- Similarly, for the evening:
\[ \text{Ways to choose from evening} = 7C1 = 7 \]

4. **Combine the Selections:**
- Since the student can choose either from the morning or the evening, we add the two results together:
\[ \text{Total ways} = \text{Ways from morning} + \text{Ways from evening} = 10 + 7 = 17 \]

5. **Final Answer:**
- Therefore, the total number of ways a student can select exactly one course, either in the morning or in the evening, is **17**.