In an examination, a candidate is required to answer 7 questions out of 12, which are divided into two groups, each containing 6 questions. One cannot attempt more than 5 questions from either group. In how many ways can he choose these questions?

Answer : There are total 13 questions out of which 10 is to be answered .The student can answer in the following ways:

⇒ 3 questions from part A and 4 from part B

⇒ 4 questions from part A and 3 from part B

⇒ 5 questions from part A and 2 from part B

⇒ 2 questions from part A and 5 from part B

⇒ total ways in the 1st case are ⁶C3      6C4

⇒ total ways in the 2nd case are ⁶C4      6C3

⇒ total ways in the 3rd case are ⁶C5      6C2

⇒ total ways in the 4th case are ⁶C2X 6C5

=6C4 X6C3+ 6C3 X6C4 X6C5 X6C2+ 6C2 X6C5

= 780 ways.