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The question asks: "How many even three-digit numbers can be formed using the digits 1, 3, 6, 7, 8, 9, where all digits are distinct?"

To solve this problem:

1. **Determine possible choices for the last digit**: 
   - Since the number must be even, the last digit must be one of the even digits from the given set. The even digits available are 6 and 8. So, there are 2 choices for the last digit.

2. **Determine possible choices for the first digit**:
   - After choosing the last digit (either 6 or 8), we have 5 digits left. The first digit can be any of these 5 digits. So, there are 5 choices for the first digit.

3. **Determine possible choices for the middle digit**:
   - After choosing the first and the last digits, 4 digits remain. The middle digit can be any of these remaining 4 digits. So, there are 4 choices for the middle digit.

4. **Calculate the total number of possibilities**:
   - The total number of three-digit even numbers that can be formed is the product of the choices for each digit:  
     \[
     5 \times 4 \times 2 = 40
     \]

So, the correct answer is **40**.

Would you like more details on this, or do you have any questions?

Here are some related questions you might be interested in:
1. How many odd three-digit numbers can be formed using the digits 1, 3, 6, 7, 8, 9 with distinct digits?
2. What is the probability of randomly forming an even number using the digits 1, 3, 6, 7, 8, 9?
3. How many even three-digit numbers can be formed if repetition of digits is allowed?
4. How many distinct three-digit numbers can be formed using all six digits?
5. If the digits 1, 3, 6, 7, 8, 9 are randomly arranged, what is the probability of forming an even number?

**Tip:** When solving permutation problems, remember to account for restrictions (like requiring the number to be even) by narrowing down choices step-by-step for each digit.

How many even three-digit numbers can be formed using the digits 1, 3, 6, 7, 8, 9, where all digits are distinct?

Explore how to calculate the total number of even three-digit numbers that can be formed using the digits 1, 3, 6, 7, 8, 9 without repeating any digits. Learn the permutation approach to solve this problem, suitable for students in Grades 8-10.

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