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?

Question

Philoid · Accepted 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 ⁶C₃⁶C₄

⇒ total ways in the 2nd case are ⁶C₄⁶C₃

⇒ total ways in the 3rd case are ⁶C₅⁶C₂

⇒ total ways in the 4th case are ⁶C₂⁶C₅

=⁶C₄⁶C₃+⁶C₃⁶C₄⁶C₅⁶C₂+ ⁶C₂⁶C₅

Applying ⁿC_r =

= 780 ways.