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?

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 nCr =


= 780 ways.


1