Question

A committee of $5$ is to be chosen from a group of $9$ people. Number of ways in which it can be formed if two particular persons either serve together or not at all and two other particular persons refuse to serve with each other, is?

• A. $41$
• B. $36$
• C. $47$
• D. $76$

Answer 1

Answer: (A)

$41$

Let $P_1,P_2$ be the persons who either serve together or not at all

$P_3,P_4$ be the people who refuse to solve with each other

Possible cases are

$(P_1,P_2,P_3)$ and two other

$(P_1,P_2,P_4)$ and two other

$(P_1,P_2)$ and $3$ others including $P_3$ and $P_4$

$P_3$ and 4 others including $P_1,P_2,P_4$

$P_4$ and 4 others including $P_1,P_2,P_3$

$P_5$ to $P_4$ are selected

${}^5{C}_2+{}^5{C}_2+{}^5{C}_3+{}^5{C}_4+{}^5{C}_4+1$

$10+10+10+5+5+1$

Total cases = $41$