A student is required to answer 6 out of 10 questions in an examination. The questions are divided into two groups, each containing 5 questions. She is not allowed to attempt more than 4 questions from each group. The number of different ways in which the student can choose the 6 questions is
Explanation:
As there are 5 questions in each section we have three different cases to be considered.
Case 1:
3 questions from section 1 and 3 questions from section 2
Number of ways = 5C3 × 5C3 = 100
Case 2:
4 questions from section 1 and 2 questions from section 2
Number of ways = 5C4 × 5C2 = 50
Case 3:
2 questions from section 1 and 4 questions from section 2
Number of ways = 5C2 × 5C4 = 50
∴ Total number of ways = 100 + 50 + 50 = 200
Hence, option (c).
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