Questions: The drama society members are voting for the type of play they will perform next season. The choices are (D)rama, (C)omedy, (M)ystery, or (G)reek tragedy. The votes are summarized in the following preference table. Number of Ballots Preference 15 13 2 30 10 1st M C D D M 2nd C M C G C 3rd D D G M G 4th G G M C D What option is selected using the Borda count method? A. Greek B. Mystery C. Comedy D. Drama

Solution Steps

The drama society members are voting for the type of play they will perform next season. The options are (D)rama, (C)omedy, (M)ystery, and (G)reek tragedy. The votes are summarized in a preference table, and we need to determine the winner using the Borda count method.

Using the Borda count method, we assign points based on the ranking of each option. The points assigned for each rank are as follows:

• 1st choice: 3 points
• 2nd choice: 2 points
• 3rd choice: 1 point
• 4th choice: 0 points

We calculate the total points for each option based on the number of ballots and the preferences:

• For option \( D \): \[ 15 \times 3 + 13 \times 2 + 2 \times 1 + 30 \times 0 + 10 \times 1 = 45 + 26 + 2 + 0 + 10 = 83 \]
• For option \( C \): \[ 15 \times 2 + 13 \times 3 + 2 \times 2 + 30 \times 1 + 10 \times 0 = 30 + 39 + 4 + 30 + 0 = 103 \]
• For option \( M \): \[ 15 \times 3 + 13 \times 2 + 2 \times 0 + 30 \times 1 + 10 \times 0 = 45 + 26 + 0 + 30 + 0 = 101 \]
• For option \( G \): \[ 15 \times 0 + 13 \times 1 + 2 \times 0 + 30 \times 2 + 10 \times 3 = 0 + 13 + 0 + 60 + 30 = 103 \]

After calculating the Borda counts, we have:

• \( D: 124 \)
• \( C: 93 \)
• \( M: 131 \)
• \( G: 72 \)

The option with the highest Borda count is \( M \) with a total of \( 131 \) points.

Final Answer