There are 10 board members on the Community Arts Council. In how many ways can a president and treasurer be chosen? Assume that no member can hold both positions at the same time.
There are 10 board members on the Community Arts Council. In how many ways can a president and treasurer be chosen? Assume that no member can hold both positions at the same time.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.CT: Chapter Test
Problem 21CT: How many ways can 4 men and 4 women stand in line if all the women are first?
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Question
![### Problem
There are 10 board members on the Community Arts Council. In how many ways can a president and treasurer be chosen? Assume that no member can hold both positions at the same time.
### Solution Explanation
To solve this problem, we need to determine the number of ways to select two different individuals from the 10 board members to fill the positions of president and treasurer.
1. **Choose the President:**
- There are 10 possible candidates for the position of president.
2. **Choose the Treasurer:**
- After the president is selected, there are 9 remaining candidates for the treasurer position (since one member has already been chosen as president and cannot hold both roles).
3. **Calculate the Total Number of Ways:**
- Multiply the number of choices for president by the number of choices for treasurer:
\[
10 \times 9 = 90
\]
Therefore, there are 90 different ways to choose a president and a treasurer from the 10 board members, with the condition that one individual cannot hold both positions simultaneously.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F151256dd-d6d4-4ed4-a322-9c74fbc712af%2Fa11ddb26-be3f-4b41-833d-4441a16a6a1c%2F54dicm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem
There are 10 board members on the Community Arts Council. In how many ways can a president and treasurer be chosen? Assume that no member can hold both positions at the same time.
### Solution Explanation
To solve this problem, we need to determine the number of ways to select two different individuals from the 10 board members to fill the positions of president and treasurer.
1. **Choose the President:**
- There are 10 possible candidates for the position of president.
2. **Choose the Treasurer:**
- After the president is selected, there are 9 remaining candidates for the treasurer position (since one member has already been chosen as president and cannot hold both roles).
3. **Calculate the Total Number of Ways:**
- Multiply the number of choices for president by the number of choices for treasurer:
\[
10 \times 9 = 90
\]
Therefore, there are 90 different ways to choose a president and a treasurer from the 10 board members, with the condition that one individual cannot hold both positions simultaneously.
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