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. He can choose the seven questions in 650 ways.

Answer 1

False
He can attempt questions in following manner
`{:("Group (A)", 2, 3, 4, 5),("Group (B)", 5, 4, 3, 2):}`
Number of ways of attempting 7 questions
`= ""^(6)C_(2) xx ""^(6)C_(5) + ""^(6)C_(3) xx ""^(6)C_(4) + ""^(6)C_(4) xx ""^(6)C_(3) + ""^(6)C_(5) xx ""^(6)C_(2)`
`= 2 (""^(6)C_(2) xx ""^(6)C_(5) + ""^(6)C_(3) xx ""^(6)C_(4))`
`= 2 (15 xx 6 + 20 xx 15)`
`= 2 (90 + 300)`
`= 2 xx 390 = 780`