How many 3-digit even numbers can be formed by using the digits 1 to 9, if no digit is repeated?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 224
A number is even when its units digit is even, so the units place is filled first, and then the other two places from the digits left (no digit repeated).
Units place: one of 2, 4, 6, 8, that is, 4 ways
Hundreds place: any of the 8 digits not yet used, 8 ways
Tens place: any of the 7 digits still left, 7 ways
Number of even 3-digit numbers \(=4\times8\times7=224\)
Tip: Fill the place with the condition (here the units place) first. Without the word ‘even’ the count would be \(9\times8\times7=504\), which is also among the options.