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?
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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