Twice during the assembly, a student is chosen at random to assist with the presentation. After the first student has finished assisting, the student returns to the group and can be chosen a second time. What is the probability that the first student chosen is a senior and the second student chosen is a sophomore?

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.