The top piece from a model of city hall is shown below.

A square pyramid. The base is 14 millimeters by 14 millimeters. The triangular sides have a base of 14 millimeters and height of 25 millimeters. The pyramid has a height of 24 millimeters.

If Serena painted all the faces of the piece of the model, including the base, what area did she paint?

Out of five men and five women, we form a committee consisting of four different people. assuming that each committee of size four is equally likely, find the probabilities of the following events: 1. the committee consists of two men and two women 2. the committee has more women than men. 3. the committee has at least one man. for the remainder of the problem assume that alice and bob are among the ten people being considered. 4. both alice and bob are members of the committee.