From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?

Answer: Option D

We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only).
∴ the Required number of ways
$$\begin{array}{rl}& =\left({}^7{C}_3\times {}^6{C}_2\right)+\left({}^7{C}_4\times {}^6{C}_1\right)+\left({}^7{C}_5\right)\\ & =\left(\frac{7\times 6\times 5}{3\times 2\times 1}\times \frac{6\times 5}{2\times 1}\right)+\left({}^7{C}_3\times {}^6{C}_1\right)+\left({}^7{C}_2\right)\\ & =525+\left(\frac{7\times 6\times 5}{3\times 2\times 1}\times 6\right)+\left(\frac{7\times 6}{2\times 1}\right)\\ & =\left(525+210+21\right)\\ & =756\end{array}$$