In a college examination, a candidate is required to answer 6 out of 10 question which are divided into two section each containing 5 questions. Further the candidates is not permitted to attempt more than 4 questions from either of the section. The number of ways in which he can make up a choice of 6 question is

Options

A. 200
B. 150
C. 100
D. 50

Answer

To solve the problem, we need to determine the number of ways a candidate can choose 6 questions from 10, adhering to the constraints given. Here's a step-by-step breakdown of the solution:

### Step 1: Understand the Problem
We have 10 questions divided into two sections (Section A and Section B), each containing 5 questions. The candidate must choose 6 questions but cannot select more than 4 questions from either section.

### Step 2: Identify Possible Combinations
Given the restriction of not selecting more than 4 questions from either section, the possible distributions of questions selected from each section are:
1. 4 questions from Section A and 2 questions from Section B
2. 3 questions from Section A and 3 questions from Section B
3. 2 questions from Section A and 4 questions from Section B

### Step 3: Calculate Each Case
Now, we will calculate the number of ways to choose questions for each case.

#### Case 1: 4 from Section A and 2 from Section B
- The number of ways to choose 4 questions from 5 in Section A:
\[ \binom{5}{4} = 5 \]
- The number of ways to choose 2 questions from 5 in Section B:
\[ \binom{5}{2} = 10 \]
- Total for this case:
\[ 5 \times 10 = 50 \]

#### Case 2: 3 from Section A and 3 from Section B
- The number of ways to choose 3 questions from 5 in Section A:
\[ \binom{5}{3} = 10 \]
- The number of ways to choose 3 questions from 5 in Section B:
\[ \binom{5}{3} = 10 \]
- Total for this case:
\[ 10 \times 10 = 100 \]

#### Case 3: 2 from Section A and 4 from Section B
- The number of ways to choose 2 questions from 5 in Section A:
\[ \binom{5}{2} = 10 \]
- The number of ways to choose 4 questions from 5 in Section B:
\[ \binom{5}{4} = 5 \]
- Total for this case:
\[ 10 \times 5 = 50 \]

### Step 4: Add All Cases Together
Now, we sum the totals from all three cases:
\[ 50 + 100 + 50 = 200 \]

### Final Answer
The total number of ways the candidate can choose 6 questions is:
\[ \boxed{200} \]