The number of all possible selections of one or more questions from 10 given questions, each question having one alternative is

Options

A. A) `3^(10)`
B. B) `2^(10)-1`
C. C) `3^(10) -1`
D. D) `2^(10)`

Answer

To solve the problem of finding the number of all possible selections of one or more questions from 10 given questions, where each question has one alternative, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Choices for Each Question**:
Each question has three possible choices:
- Select the question.
- Select the alternative of the question.
- Do not select the question at all.

2. **Calculating Total Choices for All Questions**:
Since there are 10 questions, and each question has 3 choices, the total number of combinations of selections can be calculated as:
\[ \text{Total combinations} = 3^{10} \]
This is because for each of the 10 questions, we have 3 independent choices.

3. **Excluding the Empty Selection**:
The total combinations calculated above include the scenario where none of the questions are selected (the empty selection). Since we are interested in selections of one or more questions, we need to subtract this one case from our total:
\[ \text{Valid selections} = 3^{10} - 1 \]

4. **Final Calculation**:
Now, we can compute \(3^{10}\):
\[ 3^{10} = 59049 \]
Therefore, the number of valid selections is:
\[ 59049 - 1 = 59048 \]

### Final Answer:
The number of all possible selections of one or more questions from 10 given questions is:
\[ \boxed{59048} \]