How many 3-digit even numbers can be formed using 1, 2, 3, 4, 6, 7 digits without repeating them?

Correct option is A

Given:

Digits available: $1,2,3,4,6,7$
We need to form 3-digit even numbers without repeating the digits.

Key Points:

1. A 3-digit even number must end with an even digit.
2. From the given digits, the even digits are $2,4,6$.

Steps to Solve:

1. Choose the last digit:
   Since the number must be even, the last digit can only be one of $2,4,6$.
   There are 3 choices for the last digit.

2. Choose the first digit:
   After selecting the last digit, 5 digits remain, from which we can choose any digit for the first position (excluding the already chosen last digit).
   There are 5 choices for the first digit.

3. Choose the second digit:
   After selecting the first and last digits, 4 digits remain.
   There are 4 choices for the second digit.

4. Calculate total combinations:
   Multiply the choices:

   $$\text{Total numbers}=3\times 5\times 4=60$$

Final Answer:
The total number of 3-digit even numbers that can be formed is 60.