How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?
60
Explanation
This question is similar to Example 3 in the textbook context, which shows how to count even numbers by starting with the unit's place constraint. The key insight from the context is that when forming even numbers, we should first identify which digits can occupy the unit's place (the even digits), then fill the remaining places using the multiplication principle.
Solution Steps
Step 1: Identify the even digits from the given set {1, 2, 3, 4, 6, 7}. The even digits are 2, 4, and 6. So the unit's place can be filled in 3 ways.
Step 2: After filling the unit's place, 5 digits remain. The hundred's place can be filled by any of these 5 remaining digits in 5 ways.
Step 3: After filling both unit's and hundred's places, 4 digits remain. The ten's place can be filled in 4 ways.
Step 4: By the multiplication principle (as shown in Example 3 and Example 4 of the context), total number of 3-digit even numbers = × 4 = 60.