A committee of 12 members is to be formed from 9 women and 8 men. The number of committees in which the women are in majority is 

Number of women = 9

Number of men        = 8

A committee of 12 is formed such that women are is majority

 Committee can  be  formed with (7W, 5M), (8W, 4M) (9W, 3M)

No. of committees $=9_{{\mathrm{C}}_7}\times 8_{{\mathrm{C}}_5}+9_{{\mathrm{C}}_8}\times 8_{{\mathrm{C}}_4}+9_{{\mathrm{C}}_9}\times 8_{{\mathrm{C}}_3}$

$$\begin{gathered} =36\times 56+9\times 70+1\left(56\right) \\ =2702 \end{gathered}$$