Chapter 2, Problem 44E

Consider a weighted voting system with five players ( $P_1$ through $P_5$).

a. Find the total number of coalitions in this weighted voting system.

b. How many coalitions in this weighted voting system do not include $P_1$?(Hint: Think of all the possible coalitions of the remaining players.)

c. How many coalitions in this weighted voting system do not include $P_5$? [Hint: Is this really different from (b)?]

d. How many coalitions in this weighted voting system do not include $P_1\text{ or }{P}_5$?

e. How many coalitions In this weighted voting system include both $P_1\text{ and }{P}_5$?

[Hint: Use your answers for (a) and (d).]