Question

The number of ways of choosing a committee of $2$ women & $3$ men from $5$ women & $6$ men, if Mr. $A$ refuses to serve on the committee if Mr. $B$ is a member & Mr. $B$ can only serve, if Miss $C$ is the member of the committee, is

• A. $60$
• B. $84$
• C. $124$
• D. $none$

Answer 1

The correct option is C $124$

There would be 2 calel $\to$

1) Mr. B is a member

$\Rightarrow$ Mr It implies Mirs C is a member

Now we left with 4 woman & 5 men

(And Mr. A is not willing to joins)

$\therefore$ No. of ways of choosing 1 woman & 2 men

${=}^4{C}_1{\times }^4{C}_0=24$

(2) Mr B is not a member So, we left with

5 men.

$\therefore$ No. of ways choosing 2 women & 3 men

${=}^5{C}_0{\times }^5{C}_3=100$

So, Total no. of ways $=100+24=124$