Question

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

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

Answer 1

Answer: (B)

$84$

Total no of men$=3$

Total no of women$=5$

The total no of ways$=4C_2\ast 6C_4+4C_3\ast 6C_6$

$4C_2=4!2!2!=4\ast 3\times 2!2\times 2!=6$

$6C_4=6!4!2!=6\times 5\times 4!4!\times 2=15$

$4C_3=4!3!1!=4\ast 3!3!\ast 1=4$

$6C_6=6!6!0!=1$

$4C_2\ast 6C_4+4C_3\ast 6C_6=6\ast 15+4\ast 1=80+4=84$