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    Question

    An examinee is required to answer the eight questions

    out of 16 questions which are divided into two groups each containing eight questions each and he is not permitted to answer more than six questions from any group. In how many ways can he answer the eight questions?
    A 12,740 Correct Answer Incorrect Answer
    B 12,720 Correct Answer Incorrect Answer
    C 12,470 Correct Answer Incorrect Answer
    D 12,570 Correct Answer Incorrect Answer
    E 12,750 Correct Answer Incorrect Answer

    Solution

    Required number of ways = (⁸C6 × ⁸C₂ + ⁸C5 × ⁸C₃ + ⁸C4 × ⁸C4 + ⁸C₃ × ⁸C5 + ⁸C₂ × ⁸C6)  = (28 × 28 + 56 × 56 + 70 × 70 + 56 × 56 + 28 × 28) = 12,740

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