Question

A candidate is required to answer 7 out of 12 questions which are divided into two equal groups and he is not permitted to answer more than 5 questions from each group. The number of different ways in which he can choose 7 questions is:

• A. $560$
• B. $920$
• C. $1200$
• D. $780$

Answer 1

The correct option is D $780$

Question(Group 1) (6)	Question(Group 2) (6)	Number of ways of selection of 7 question
5	2	${}^6{C}_5{.}^6{C}_2=90$
4	3	${}^6{C}_4{.}^6{C}_3=300$
3	4	${}^6{C}_3{.}^6{C}_4=300$
2	5	${}^6{C}_2{.}^6{C}_5=90$

Hence required number of ways $=90+300+300+90=780$