SOLUTION: Each state of the 50 in the United States has two senators. In how many ways may a majority be achieved in the U.S. Senate? Ignore the possibility of absence or abstention. Assum

Algebra ->  Permutations -> SOLUTION: Each state of the 50 in the United States has two senators. In how many ways may a majority be achieved in the U.S. Senate? Ignore the possibility of absence or abstention. Assum      Log On


   

Question 1122845: Each state of the 50 in the United States has two senators. In how many ways may
a majority be achieved in the U.S. Senate? Ignore the possibility of absence or
abstention. Assume that all senators are present and voting.
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Each senator can vote either of 2 ways.

The number of different ways the 100 senators can vote is 2^100.

That total number of ways, 2^100, is equal to

100C0 + 100C1 + 100C2 + ... + 100C99 + 100C100

The only way not to get a majority (one way or the other) is if the vote is 50-50. The number of ways that can happen is 100C50.

So the number of ways to get a majority (one way or the other) is then

2^100 - 100C50

If you mean the number of ways of getting a majority "yes" votes, it is

(2^100 - 100C50)/2