A committee of 5 persons is to be formed from 6 men and 4 women. In how many ways can this be done when at least 2 women are included ?

When at least 2 women are included.

The committee may consist of 3 women, 2 men : It can be done in   $4C3*6C2$  ways

or, 4 women, 1 man : It can be done in   $4C4*6C1$ways

or, 2 women, 3 men : It can be done in $4C2*6C3$ ways.

Total number of ways of forming the committees

=  $4C2*6C3+4C3*6C2+4C4*6C1$

= 6 x 20 + 4 x 15 + 1x 6

= 120 + 60 + 6 =186