Shown below are the 2018 NCAA Women's Basketball Rankings for Week 15 (Feb. 12) by the AP Poll and the USA Today Coaches Poll.
The polls show the top 25 teams with their records and the number of points from the voters. The points
are based on 25 points for a first place vote, 24 points for a second place vote, ... through one point for a
25th-place vote. Connecticut received all the first place votes from the voters for a perfect score of 800 in both polls.
But I wondered how the voters voted for the second place team, Mississippi State. Give all the possibilities that
could have happened so that Mississippi state received 765 points in the AP Poll and 766 points in the USA Today Poll.
Hint: You must first determine the number of voters in each poll.
Solution to the Problem:
First, you can determine that there are 32 voters in each poll by taking the
total points that Connecticut received (800) and divide it by 25: 800/25 = 32. So,
the total number of votes for Mississippi State will be 32. They could not have received
all the 2nd place votes because their score would have been 32 x 24 = 768.
For the AP Poll, there are three ways in which the voters could have voted:
| 2nd (24 pts)
|
3rd (23 pts)
|
4th (22 pts)
|
5th (21 pts)
|
| 31
|
0
|
0
|
1
|
| 30
|
1
|
1
|
0
|
| 29
|
3
|
0
|
0
|
For the USA TODAY Poll, there are only two ways in which they could have voted:
| 2nd (24 pts)
|
3rd (23 pts)
|
4th (22 pts)
|
| 31
|
0
|
1
|
| 30
|
2
|
0
|
Correctly solved by: