How many combinations of two digit number having 8 can be made from the following numbers?
8, 5, 2, 1, 7, 6

Options

A. 9
B. 11
C. 10
D. 12

Explanation

To find how many combinations of two-digit numbers can be made that include the digit 8 from the numbers 8, 5, 2, 1, 7, and 6, we will consider two cases: when 8 is in the tens place and when 8 is in the units place.

### Step-by-Step Solution:

1. **Identify the available digits**: The available digits are 8, 5, 2, 1, 7, and 6. This gives us a total of 6 digits.

2. **Case 1: 8 in the tens place**:
- If 8 is in the tens place, the two-digit number will look like this: 8X, where X is any of the remaining digits.
- The remaining digits available for X are 5, 2, 1, 7, and 6 (5 options).
- Therefore, the combinations for this case are: 85, 82, 81, 87, 86.
- Total combinations for this case = 5.

3. **Case 2: 8 in the units place**:
- If 8 is in the units place, the two-digit number will look like this: XY8, where X is any of the available digits except 8 (since we cannot repeat the digit in the tens place).
- The available digits for X are 5, 2, 1, 7, and 6 (5 options).
- Therefore, the combinations for this case are: 58, 28, 18, 78, 68.
- Total combinations for this case = 5.

4. **Case 3: Both digits are 8**:
- The only number that can be formed with both digits being 8 is 88.
- Total combinations for this case = 1.

5. **Total combinations**:
- Add the combinations from all cases:
- Case 1: 5 combinations
- Case 2: 5 combinations
- Case 3: 1 combination
- Total = 5 + 5 + 1 = 11 combinations.

### Final Answer:
The total number of combinations of two-digit numbers having 8 is **11**.