In how many ways a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women ?

Answer: Option C

Required number of ways
$$\begin{array}{rl}& \left({}^8{C}_5\times {}^{10}{C}_6\right)+\left({}^8{C}_3\times {}^{10}{C}_4\right)\\ & =\frac{8\times 7\times 6}{3!}\times \frac{10\times 9\times 8\times 7}{4!}\\ & =\frac{8\times 7\times 6}{3\times 2\times 1}\times \frac{10\times 9\times 8\times 7}{4\times 3\times 2\times 1}\\ & =11760\end{array}$$