The number of all the possible selections which a student can make for answering one or more questions out of eight given questions in a paper, when each question has an altrenative, is

Options

A. 256
B. 6560
C. 6561
D. none of these

Answer

To solve the problem of determining the number of possible selections a student can make for answering one or more questions out of eight given questions, where each question has an alternative, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Choices**:
Each of the 8 questions has 3 options:
- Answer using option A
- Answer using option B
- Do not answer the question at all

2. **Calculating Total Choices**:
Since there are 3 choices for each of the 8 questions, the total number of ways to select answers (including the option of not answering any question) can be calculated using the formula:
\[ \text{Total Choices} = 3^8 \]

3. **Calculating \(3^8\)**:
Now, we need to calculate \(3^8\):
\[ 3^8 = 6561 \]

4. **Excluding the Invalid Case**:
The problem states that the student must answer at least one question. The only invalid case is when the student chooses not to answer any of the questions at all. This case counts as 1 way (where the student selects "no answer" for all questions).

5. **Final Calculation**:
To find the valid selections, we subtract the invalid case from the total choices:
\[ \text{Valid Selections} = 6561 - 1 = 6560 \]

6. **Conclusion**:
Therefore, the number of all possible selections which a student can make for answering one or more questions out of the eight given questions is:
\[ \boxed{6560} \]