In a weighted voting system with 20 voters, how many distinct coalitions would there be in which exactly eight members voted YES?
A) 12
B) 56
C) 160
D) 125,970

Question

Quizplus · Accepted Answer

The number of distinct coalitions in which exactly eight members voted YES out of 20 voters can be calculated using the combination formula, which is C(n, k) = n! / [k!(n-k)!], where n is the total number of items (in this case, voters), and k is the number of items to be chosen (in this case, YES votes). So, C(20, 8) = 20! / [8!(20-8)!] = 125,970.

In a Weighted Voting System with 20 Voters, How Many