Question

How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?

Hint:

For a 3-digit even number, the last digit must be even, and other digits can be any of the given digits.

Answer 1

Step 1: Define the requirements for the 3-digit even number.
For a number to be even, its last digit must be one of the even digits: 2, 4, or 6.
Step 2: Determine the possibilities for each digit.
- The last digit (ones place) can be any of 3 even digits: 2, 4, or 6. So, there are 3 choices for the last digit. - The first digit (hundreds place) can be any digit from 1 to 6 (since the number must be a 3-digit number). Therefore, there are 6 choices for the first digit. - The second digit (tens place) can also be any digit from 1 to 6. So, there are 6 choices for the second digit.
Step 3: Calculate the total number of 3-digit even numbers.
The total number of 3-digit even numbers is the product of the choices for each digit: \[ \text{Total numbers} = 6 \times 6 \times 3 = 108 \]