Question

From a group of $7$ men and $6$ women, five persons are to be selected to form a committee so that at least three men are in the committee. In how many ways can it be done?

• A. $624$
• B. $702$
• C. $756$
• D. $812$

Answer 1

Answer: (C)

$756$

Case $1:$ $3$ Men, $2$ Women

$\Rightarrow$ ${}^7{C}_3\times {}^6{C}_2=35\times 15=525$

Case $2:$ $4$ Men, $1$ Women

$\Rightarrow$ ${}^7{C}_4\times {}^6{C}_1=35\times 6=210$

Case $3:$ $5$ Men, $0$ Women

$\Rightarrow$ ${}^7{C}_5=21$

$\Rightarrow$ Total $=525+210+21$

$=756$

Hence, the answer is $756.$