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

Answer: (C)

$124$

First of all number of ways.

Committees can be founded $={}^6{C}_3\times {}^5{C}_2$

Now, we remove committees with both A and B $=4\times {}^5{C}_2$

again we need to remove committees with B and not C $={}^5{C}_2\times 4.$

Now we shall add the committees with A, not C as it has been subtracted twice $=4\times {}^4{C}_2$

No. of ways $={}^6{C}_3\times {}^5{C}_2-4\times {}^5{C}_2-{}^5{C}_2\times 4+4\times {}^4{C}_2$

$=124.$

Hence, the answer is $=124.$