Question
A high school debate team must elect a president, vice president, and treasurer from its 12
members. How many ways can they be chosen?
A.220
B.36
C.1,320
D.1,728
Best answer
members. How many ways can they be chosen?
A.220
B.36
C.1,320
D.1,728
Best answer
Answers
GPT-4o mini
To determine how many ways a high school debate team can elect a president, vice president, and treasurer from its 12 members, we need to consider the fact that these positions are distinct (i.e., the order matters).
1. **Choosing the President:** There are 12 options for the president.
2. **Choosing the Vice President:** After electing the president, 11 members remain. Thus, there are 11 options for the vice president.
3. **Choosing the Treasurer:** After electing both the president and the vice president, 10 members remain. Therefore, there are 10 options for the treasurer.
The total number of ways to elect the three officers can be calculated by multiplying the number of choices available at each step:
\[
\text{Total Ways} = 12 \times 11 \times 10
\]
Calculating this gives:
\[
12 \times 11 = 132
\]
\[
132 \times 10 = 1320
\]
Thus, the total number of ways to choose a president, vice president, and treasurer is \(1320\).
The correct answer is **C. 1,320**.
1. **Choosing the President:** There are 12 options for the president.
2. **Choosing the Vice President:** After electing the president, 11 members remain. Thus, there are 11 options for the vice president.
3. **Choosing the Treasurer:** After electing both the president and the vice president, 10 members remain. Therefore, there are 10 options for the treasurer.
The total number of ways to elect the three officers can be calculated by multiplying the number of choices available at each step:
\[
\text{Total Ways} = 12 \times 11 \times 10
\]
Calculating this gives:
\[
12 \times 11 = 132
\]
\[
132 \times 10 = 1320
\]
Thus, the total number of ways to choose a president, vice president, and treasurer is \(1320\).
The correct answer is **C. 1,320**.