Question

The number of ways of choosing a committee of two women and three men from five women and six men, if Mr. A refuses to serve on the committee if Mr. B is a member and Mr. B can only serve, if Miss C is the member of the committee is

• A. $60$
• B. $84$
• C. $124$
• D. None of these

Answer 1

The correct option is C $124$

Case I: Mr. 'B' is present
$\because$ Mr. 'B' is present then according to the given condition Mrs 'C' needs to be in the committee and Mr. A should not be in the committee
$\Rightarrow$ 'A' is excluded and 'C' included
Hence, the number of ways is ${}^4{C}_2{}^4{C}_1=24$.

Case II: Mr. 'B' is absent
$\because$ Mr. 'B' is absent then according to the given condition Mrs 'C' can be in committee or not and Mr. A can be in the committee or not
$\Rightarrow$ No constraint
Hence, the number of ways is ${}^5{C}_3{}^5{C}_2=100$
$\therefore$ Total $=124$