A student council consists of 15 students. (a) How many ways can a committee of eight be selected from the membership of the council? As in Example 9.5.4, since a committee chosen from the members of the council is a subset of the council, the number of ways to select the committee is . (b) Two council members have the same major and are not permitted to serve together on a committee. How many ways can a committee of eight be selected from the membership of the council? As in Example 9.5.6, let A and B be the two council members who have the same major. The number of ways to select a committee of eight that contains A and not B is . The number of ways to select a committee of eight that contains B and not A is . The number of ways to select a committee of eight that contains neither A nor B is . The total number of committees of eight that can be selected from the membership of the council is the ---Select--- sum product of the number of committees with A and not B, B and not A, and neither A nor B. Thus, the answer is