Question

A candidate is required to answer six out of $10$ questions, which are divided into two groups, each containing five questions. He is not permitted to attempt more than four questions from either group. The number of different ways in which the candidates can choose six questions is

• A. $50$
• B. $150$
• C. $200$
• D. $250$

Answer 1

The correct option is C $200$

The number of ways the candidate can choose questions under the given conditions is enumerated below.

Group $1$	Group $2$	Number of ways
$4$	$2$	${(}^5{C}_4\left){(}^5{C}_2\right)=50$
$3$	$3$	${(}^5{C}_3\left){(}^5{C}_3\right)=100$
$2$	$4$	${(}^5{C}_2\left){(}^5{C}_4\right)=50$
	Total number of ways	$200$