How many three-digit even numbers can be formed using the digits 1, 2, 3, 4 and 5, when repetition of digits is not allowed?

Note: Repetition is not allowed

For a three-digit even, the unit place has two possibilities.

Case 1: The unit place is 2 i.e. _ _ 2

Now, Hundreds place can be filled in 4 ways (1,3,4,5) and Tens place can be filled in 3 ways.

Case 1 $=4 \times 3 = 12$ ways

Case 2: The unit place is 4 i.e. _ _ 4

Now, Hundreds place can be filled in 4 ways (1,2,3,5) and Tens place can be filled in 3 ways.

Case 2 $=4 \times 3 = 12$ ways

Total cases $= 12 + 12 = 24$

Hence, the correct option is Option 3.