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

Solution (By Examveda Team)

Required number of ways
$$\eqalign{ & \left( {{}^8{C_5} \times {}^{10}{C_6}} \right) + \left( {{}^8{C_3} \times {}^{10}{C_4}} \right) \cr & = \frac{{8 \times 7 \times 6}}{{3!}} \times \frac{{10 \times 9 \times 8 \times 7}}{{4!}} \cr & = \frac{{8 \times 7 \times 6}}{{3 \times 2 \times 1}} \times \frac{{10 \times 9 \times 8 \times 7}}{{4 \times 3 \times 2 \times 1}} \cr & = 11760 \cr} $$