How many different 5 persons committees can be formed each containing at least two women and at least one man from a set of 10 women and 15 men
Containing 2 women and 3 men : $\displaystyle 10C2\times15C3=20475$
Containing 3 women and 2 men : $\displaystyle 10C3\times15C2=12600
$
Containing 4 women and 1 man : $\displaystyle 10C4\times15C1=3150$
Total choices$\displaystyle =36225$