A question paper consists of two sections having respectively 3 and 5 questions. The following note is given on the paper. "It is not necessary to attempt all the questions". One question from each section is compulsory. In how many ways, a candidate can select the question?

Options

A. 38
B. 217
C. 256
D. 320

Answer

To solve the problem, we need to determine the number of ways a candidate can select questions from two sections of a question paper, with the condition that one question from each section is compulsory.

### Step-by-Step Solution:

1. **Identify the Sections and Questions**:
- Section A has 3 questions.
- Section B has 5 questions.

2. **Select One Compulsory Question from Each Section**:
- From Section A, the candidate must select 1 question out of 3. The number of ways to do this is:
\[ \text{Ways from Section A} = 3 \]
- From Section B, the candidate must select 1 question out of 5. The number of ways to do this is:
\[ \text{Ways from Section B} = 5 \]

3. **Calculate the Total Ways to Select Compulsory Questions**:
- Since one question from each section is compulsory, the total number of ways to select these compulsory questions is:
\[ \text{Total Compulsory Ways} = \text{Ways from Section A} \times \text{Ways from Section B} = 3 \times 5 = 15 \]

4. **Select Additional Questions**:
- After selecting the compulsory questions, the candidate can choose to select additional questions from each section, including the option to select none.
- For Section A (3 questions), the candidate can select:
- No additional questions (1 way)
- 1 additional question (3 ways)
- 2 additional questions (3 ways)
- All 3 questions (1 way)
- The total ways to select additional questions from Section A is:
\[ 1 + 3 + 3 + 1 = 8 \text{ ways} \]

- For Section B (5 questions), the candidate can select:
- No additional questions (1 way)
- 1 additional question (5 ways)
- 2 additional questions (10 ways)
- 3 additional questions (10 ways)
- 4 additional questions (5 ways)
- All 5 questions (1 way)
- The total ways to select additional questions from Section B is:
\[ 1 + 5 + 10 + 10 + 5 + 1 = 32 \text{ ways} \]

5. **Combine All Selections**:
- Now, we multiply the total ways to select compulsory questions by the ways to select additional questions from both sections:
\[ \text{Total Ways} = \text{Total Compulsory Ways} \times \text{Ways to Select Additional from A} \times \text{Ways to Select Additional from B} \]
\[ \text{Total Ways} = 15 \times 8 \times 32 \]

6. **Calculate the Final Result**:
- Now, we calculate:
\[ 15 \times 8 = 120 \]
\[ 120 \times 32 = 3840 \]

### Final Answer:
The total number of ways a candidate can select the questions is **3840**.