In a college examination, a candidate is required to answer 6 out of 10 questions which are divided into two sections each containing 5 questions. Further the candidate 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 questions, is

# In a college examination, a candidate is required to answer 6 out of 10 questions which are divided into two sections each containing 5 questions. Further the candidate 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 questions, is

1. A

200

2. B

320

3. C

300

4. D

400

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### Solution:

The required number of ways

${=}^{5}{C}_{4}{\cdot }^{5}{C}_{2}{+}^{5}{C}_{3}{\cdot }^{5}{C}_{3}{+}^{5}{C}_{2}{\cdot }^{5}{C}_{4}=50+100+50=200$.

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