The number of even numbers of four digits that can be formed using the digits 0, 1, 2, 3, 4 and 5 is

Options

A. 180
B. 156
C. 144
D. 198

Answer

To find the number of even four-digit numbers that can be formed using the digits 0, 1, 2, 3, 4, and 5, we need to consider the conditions for forming a four-digit number and the requirement that the number must be even. The even digits available are 0, 2, and 4.

### Step-by-Step Solution:

1. **Identify the even digits**: The even digits we can use as the last digit (unit place) are 0, 2, and 4.

2. **Case 1: Last digit is 0**:
- The first digit can be any of the digits 1, 2, 3, 4, or 5 (0 cannot be the first digit).
- Choices for the first digit: 5 options (1, 2, 3, 4, 5).
- Choices for the second digit: 4 remaining options (since one digit is already used).
- Choices for the third digit: 3 remaining options.
- Total for this case:
\[ 5 \times 4 \times 3 = 60 \]

3. **Case 2: Last digit is 2**:
- The first digit can be any of the digits 1, 3, 4, or 5 (0 cannot be the first digit, and 2 is already used).
- Choices for the first digit: 4 options (1, 3, 4, 5).
- Choices for the second digit: 4 remaining options (0 can be included now).
- Choices for the third digit: 3 remaining options.
- Total for this case:
\[ 4 \times 4 \times 3 = 48 \]

4. **Case 3: Last digit is 4**:
- The first digit can be any of the digits 1, 2, 3, or 5 (0 cannot be the first digit, and 4 is already used).
- Choices for the first digit: 4 options (1, 2, 3, 5).
- Choices for the second digit: 4 remaining options (0 can be included now).
- Choices for the third digit: 3 remaining options.
- Total for this case:
\[ 4 \times 4 \times 3 = 48 \]

5. **Calculate the total number of even four-digit numbers**:
- Total = Case 1 + Case 2 + Case 3
- Total = \(60 + 48 + 48 = 156\)

### Final Answer:
The total number of even four-digit numbers that can be formed using the digits 0, 1, 2, 3, 4, and 5 is **156**.