Which is the least even number of 5-digits that can be formed by 2, 0, 5, 6 and 1?

Options

A. 10562
B. 10652
C. 10256
D. 16052

Answer

To find the least even number of 5-digits that can be formed using the digits 2, 0, 5, 6, and 1, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Even Digits**:
The even digits available are 0, 2, and 6. Since we need a 5-digit number, the last digit must be one of these even digits to ensure the number is even.

2. **Choose the Last Digit**:
To form the least number, we should choose the smallest even digit as the last digit. However, if we choose 0 as the last digit, it would not be a 5-digit number. Therefore, we will consider 2 or 6 as the last digit.

3. **Choosing the Last Digit as 2**:
If we choose 2 as the last digit, we are left with the digits 0, 5, 6, and 1 to form the first four digits. The smallest digit we can use as the first digit (to ensure it's a 5-digit number) is 1.

4. **Arrange the Remaining Digits**:
After using 1 as the first digit, we have 0, 5, and 6 left. The smallest arrangement of these digits is 0, 5, and 6. So, we arrange them in ascending order after 1.

5. **Form the Number**:
Putting it all together, we have:
- First digit: 1
- Second digit: 0
- Third digit: 5
- Fourth digit: 6
- Last digit: 2

Therefore, the number formed is **10562**.

6. **Check if it's the Least Even Number**:
Now, we check if there is any other arrangement that could give a smaller number. If we had chosen 6 as the last digit, the smallest arrangement would still yield a larger number than 10562.

Thus, the least even number of 5-digits that can be formed by the digits 2, 0, 5, 6, and 1 is **10562**.