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. The number of ways in which he can choose the 7 questions is –

• A. 650
• B. 780
• C. 720
• D. None

Answer 1

Answer: (B)

780

Answer 2

6A, 6B. Not more than 5 from either

(5A, 2B) + (4A, 3B) + (3A, 4B) + (2A, 5B)

= (⁶C₅, ⁶C₂) + ( ) + ( ) + ( )

= (6 × 15) + (15 × 20) + 20 × 15 + (15 × 6)

= 780.