Question 4 There is a committee made of five members. How many ways can they select a president, a vice president and a secretary? 20 60 10 Onone of these answers
Question 4 There is a committee made of five members. How many ways can they select a president, a vice president and a secretary? 20 60 10 Onone of these answers
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Election of Officers in a Committee**
**Question 4**
There is a committee made up of five members. How many ways can they select a president, a vice president, and a secretary?
- 20
- 60
- 10
- None of these answers
**Explanation:**
To solve this problem, consider the number of choices available for each position:
1. **President:** There are 5 possible choices for the president because all 5 members are eligible.
2. **Vice President:** After the president is selected, 4 members remain, so there are 4 choices for the vice president.
3. **Secretary:** After selecting the president and vice president, 3 members remain, leaving 3 choices for the secretary.
Calculate the total number of ways to select the officers by multiplying the number of choices for each position:
\[ 5 \times 4 \times 3 = 60 \]
Thus, there are 60 different ways to select a president, a vice president, and a secretary. Therefore, the correct answer is **60**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F299e6f79-faf6-440b-9603-5c3d9de5a70e%2F0db02d5e-b462-4117-a9fa-714aa2d4ee4d%2F8sjtgq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Election of Officers in a Committee**
**Question 4**
There is a committee made up of five members. How many ways can they select a president, a vice president, and a secretary?
- 20
- 60
- 10
- None of these answers
**Explanation:**
To solve this problem, consider the number of choices available for each position:
1. **President:** There are 5 possible choices for the president because all 5 members are eligible.
2. **Vice President:** After the president is selected, 4 members remain, so there are 4 choices for the vice president.
3. **Secretary:** After selecting the president and vice president, 3 members remain, leaving 3 choices for the secretary.
Calculate the total number of ways to select the officers by multiplying the number of choices for each position:
\[ 5 \times 4 \times 3 = 60 \]
Thus, there are 60 different ways to select a president, a vice president, and a secretary. Therefore, the correct answer is **60**.
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