Problem

Counting Votes Fifteen experts are voting to determine the best convertible of the y...

Counting Votes Fifteen experts are voting to determine the best convertible of the year. The choices are a Porsche Carrera, a Chrysler Crossfire, and a Nissan Roadster. The experts will rank the three cars 1st, 2nd, and 3rd. There are three common ways to determine the winner:

a. Plurality: The car with the most first-place votes (preferences) is the winner.

b. Instant runoff: The car with the least number of preferences is eliminated. Then the ballots for which the eliminated car is first are revised so that the second-place car is moved to first. Finally, the car with the most preferences is the winner.

c. The point system: Two points are given for each time a car is ranked first place on a ballot, one point for each time the car appears in second place on a ballot, and no points for third place.

When the ballots were cast, the Porsche won when plurality was used, the Chrysler won when instant runoff was used, and the Nissan won when the point system was used. Determine 15 actual votes for which this result would occur.

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