In a weighted voting system with eight voters, how many coalitions would there be in which exactly five members voted YES?
A) 32
B) 40
C) 56
D) 256

Question

Quizplus · Accepted Answer

The formula for the number of coalitions with k members in a weighted voting system with n voters is given by:

$$\sum_{i=k}^{n} \binom{n}{i}$$

For k = 5 and n = 8, we get the following calculation:

$$\sum_{i=5}^{8}\binom{8}{i} = \binom{8}{5} + \binom{8}{6} + \binom{8}{7} + \binom{8}{8} = 56$$

Therefore, there are 56 different coalitions in which exactly five members voted YES. The best choice is (C).

In a Weighted Voting System with Eight Voters, How Many