Question

How many 4 digit even numbers can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated ?

• A. 24
• B. 42
• C. 36
• D. 48

Answer 1

Answer:

D. 48

Answer: 48

A 4-digit number has four places to fill: [Thousands] [Hundreds] [Tens] [Units]

1. Step 1: Fill the Units place
   For a number to be even, its units digit must be an even number. Out of the given digits (1, 2, 3, 4, 5), the even options are 2 and 4.

   • Ways to fill the units place = 2 (either 2 or 4).

2. Step 2: Fill the remaining places
   Since repetition is not allowed, we have used 1 digit out of 5, leaving 4 digits available.

   • Thousands place: 4 ways (any of the remaining 4 digits).

   • Hundreds place: 3 ways (any of the remaining 3 digits).

   • Tens place: 2 ways (any of the remaining 2 digits).

3. Step 3: Multiply the possibilities
   $\text{Total even numbers} = 4 \times 3 \times 2 \times 2 = \mathbf{48}$