4people are to be chosen from 10 men and 12 women to form a committee which contains at leat two women. how many different ways can the committee be formed? if, among the 10 men and 12 women, mr. and mrs. smith can not both be selected, then how many different ways can the committee be formed?

The architect's side view drawing of a saltbox-style house shows a post that supports the roof ridge. the support post is 8 ft tall. the distance from the front of the house to the support post is less than the distance from the post to the back of the house. how far from the front of the house is the support post positioned?