In a monthly test, the teacher decides that there will be three questions, one from each of Exercises 5, 6 and 7 of the text book. If there are 12 questions in Exercise 5, 18 in Exercise 6 and 9 in Exercise 7, in how many ways can the three questions be selected ?

Answer

To solve the problem of selecting one question from each of the three exercises, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the number of questions in each exercise:**
- Exercise 5 has 12 questions.
- Exercise 6 has 18 questions.
- Exercise 7 has 9 questions.

2. **Determine the selection process:**
- We need to select one question from Exercise 5, one from Exercise 6, and one from Exercise 7.

3. **Calculate the number of ways to select questions:**
- The number of ways to select one question from Exercise 5 is \( 12C1 \), which is simply 12.
- The number of ways to select one question from Exercise 6 is \( 18C1 \), which is simply 18.
- The number of ways to select one question from Exercise 7 is \( 9C1 \), which is simply 9.

4. **Multiply the number of choices together:**
- The total number of ways to select the three questions is given by:
\[ \text{Total ways} = (12C1) \times (18C1) \times (9C1) = 12 \times 18 \times 9 \]

5. **Perform the multiplication:**
- First, calculate \( 12 \times 18 = 216 \).
- Then, multiply \( 216 \times 9 = 1944 \).

6. **Final Answer:**
- Therefore, the total number of ways to select the three questions is **1944**.