Question

There are $7$ Men and $6$ Women. In how many ways can we select $5$ members in which at least $3$ men should be there:

• (A) $836$
• (B) $256$
• (C) $495$
• (D) $756$

Answer 1

The Correct Option is D

Explanation:
There will be $3$ cases for calculating the number of ways to form a committee is as follows,Case $1:3$ Men, $2$ WomenFor selecting $3$ men out of $7$ and $2$ women out of $6$ to form the $5$ people committee, we can use the formulas given in the hint as follows,$={}^7{C}_3\times {}^6{C}_2$$=35\times 15$$=525$Case $2:4$ Men, $1$ WomanFor selecting $4$ men out of $7$ and $1$ woman out of $6$ to form thee $5$ people committee, we can use the formulas given in the hint as follows$={}^7{C}_4\times {}^6{C}_1$$=35\times 6$$=210$Case $3:5$ Men, $0$ WomenFor selecting $5$ men out of $7$ and $0$ women out of $6$ to form thee $5$ people committee, we can use the formulas given in the hint as follows,$={}^7{C}_5\times {}^6{C}_0$$=21\times 1$$=21$Total $=525+210+21=756$Hence, the correct option is (D).