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Question
A candidate is required to answer 7 questions out of 12 questions, which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. Find the number of different ways of doing question
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Solution
Total number of questions = 12
Number of questions in each group = 6
7 questions are to be attempted but not more than 5 questions from either group
∴ Total number of ways = 6C5 × 6C2 × 6C4 × 6C3 + 6C3 × 6C4 + 6C2 × 6C5
= 2[6C5 × 6C2 + 6C4 × 6C3]
= `2[6 xx (6.5)/(2.1) + (6*5*4*3)/(4*3*2*1) xx (6*5*4)/(3*2*1)]`
= 2[6 × 15 + 15 × 20]
= 2[90 + 300]
= 2 × 380
= 780
Hence, the total number of ways = 780
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