The number of 3 digit even numbers that can be formed by using the digits 1 2 3 4 and 5 is given by

Options

A. 50
B. 52
C. 48
D. none of these

Answer

To find the number of 3-digit even numbers that can be formed using the digits 1, 2, 3, 4, and 5, we need to consider the conditions for a number to be even. An even number must end with an even digit. In this case, the even digits available are 2 and 4.

### Step-by-Step Solution:

1. **Identify the last digit**: Since we want to form an even number, the last digit can either be 2 or 4.

2. **Case 1: Last digit is 2**:
- If the last digit is 2, we have two remaining positions (the hundreds and tens places) to fill.
- We can use any of the 5 digits (1, 2, 3, 4, 5) for the first two positions since repetition is allowed.
- Therefore, for the first position (hundreds place), we have 5 choices.
- For the second position (tens place), we also have 5 choices.
- Thus, the total number of combinations when the last digit is 2 is:
\[ 5 \text{ (choices for hundreds)} \times 5 \text{ (choices for tens)} \times 1 \text{ (fixed last digit)} = 25 \]

3. **Case 2: Last digit is 4**:
- Similarly, if the last digit is 4, we again have two remaining positions to fill.
- For the first position (hundreds place), we have 5 choices.
- For the second position (tens place), we also have 5 choices.
- Thus, the total number of combinations when the last digit is 4 is:
\[ 5 \text{ (choices for hundreds)} \times 5 \text{ (choices for tens)} \times 1 \text{ (fixed last digit)} = 25 \]

4. **Total combinations**:
- Now, we add the total combinations from both cases:
\[ 25 \text{ (last digit 2)} + 25 \text{ (last digit 4)} = 50 \]

### Final Answer:
The total number of 3-digit even numbers that can be formed using the digits 1, 2, 3, 4, and 5 is **50**.

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