Question

The no of ways of choosing a of committee of $2$ women & $3$ men from $5$ women & $6$ men, if Mr. A refuses to serve if B Mr. B is a member & Mr. B will only serve if Miss. C is a member, is -

• A. $60$
• B. $64$
• C. $34$
• D. $124$

Answer 1

Answer: (D)

$124$

The committee has to be choosen in such a way that there are $2$ women from $5$ and $3$ men from $6$ men.

Case 1:

All committes , the no: of member will be =${}^6{C}_3{\times }^5{C}_2$=200.

Removal of the committee with both A and B =4${\times }^5{C}_2$=$40$ ways.

Removal of committee with B and not C =${}^5{C}_2\times 4$=$40$ ways.

Inclusion/exclusion: add the committee with $A,B$and $C$ : $4$${\times }^4{C}_2$=$4$

$\therefore$ Total ways =$200-40-40+4=124$ ways.