How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?
108
Explanation
A 3-digit number has three places: hundreds place, tens place, and units place. For a number to be even, the units place must contain an even digit.
From the digits 1, 2, 3, 4, 5, 6, the even digits are 2, 4, and 6. So the units place can be filled in 3 ways. Since digits can be repeated, the tens place can be filled by any of the 6 digits in 6 ways, and the hundreds place can also be filled by any of the 6 digits in 6 ways.
By the multiplication principle, the total number of 3-digit even numbers = × 3 = 108.
Solution Steps
Step 1: Identify the three places in a 3-digit number: hundreds, tens, and units.
Step 2: For an even number, the units place must have an even digit. From digits 1-6, even digits are 2, 4, 6 → 3 ways.
Step 3: Since digits can be repeated, tens place can be filled by any of 6 digits → 6 ways.
Step 4: Similarly, hundreds place can be filled by any of 6 digits → 6 ways.
Step 5: By multiplication principle, total numbers = × 3 = 108.