COMBINATIONS AND PERMUTATIONS 4. In a community chorus, 10 people are candidates for the board of directors. The board has 6 members: 4 officers (president, vice president, secretary, and treasurer) and 2 at-large members (who don't have an office). Part A: First, the four officers are chosen. In how many ways can 4 of the 10 candidates be chosen to be president, vice president, secretary, and treasurer? Is this a combination or a permutation? Explain. Part B: Next, 2 of the remaining 6 candidates are chosen to be the at-large board members. In how many ways can they be chosen? Is this a combination or a permutation? Explain. Part C: The chorus decides to choose the 2 at-large board members from the 6 remaining candidates randomly. What is a fair way to do this?
COMBINATIONS AND PERMUTATIONS 4. In a community chorus, 10 people are candidates for the board of directors. The board has 6 members: 4 officers (president, vice president, secretary, and treasurer) and 2 at-large members (who don't have an office). Part A: First, the four officers are chosen. In how many ways can 4 of the 10 candidates be chosen to be president, vice president, secretary, and treasurer? Is this a combination or a permutation? Explain. Part B: Next, 2 of the remaining 6 candidates are chosen to be the at-large board members. In how many ways can they be chosen? Is this a combination or a permutation? Explain. Part C: The chorus decides to choose the 2 at-large board members from the 6 remaining candidates randomly. What is a fair way to do this?
Chapter8: Sequences, Series,and Probability
Section8.6: Counting Principles
Problem 40E: Choosing Officers From a pool of 12 candidates, the offices of president, vice-president, secretary,...
Question
Please give detailed and easy understanding answers. If possible can you please do it on a paper
![COMBINATIONS AND PERMUTATIONS
4. In a community chorus, 10 people are candidates for the board of directors. The
board has 6 members: 4 officers (president, vice president, secretary, and treasurer)
and 2 at-large members (who don't have an office).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F64603e60-42eb-4c47-8bd7-f2f5959e2344%2F5a1eb407-f3cf-4512-bc07-84d6511df9a3%2Fj1akyk6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:COMBINATIONS AND PERMUTATIONS
4. In a community chorus, 10 people are candidates for the board of directors. The
board has 6 members: 4 officers (president, vice president, secretary, and treasurer)
and 2 at-large members (who don't have an office).
![Part A: First, the four officers are chosen. In how many ways can 4 of the 10
candidates be chosen to be president, vice president, secretary, and treasurer? Is this
a combination or a permutation? Explain.
Part B: Next, 2 of the remaining 6 candidates are chosen to be the at-large board
members. In how many ways can they be chosen? Is this a combination or a
permutation? Explain.
Part C: The chorus decides to choose the 2 at-large board members from the 6
remaining candidates randomly. What is a fair way to do this?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F64603e60-42eb-4c47-8bd7-f2f5959e2344%2F5a1eb407-f3cf-4512-bc07-84d6511df9a3%2Fhahw6li_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Part A: First, the four officers are chosen. In how many ways can 4 of the 10
candidates be chosen to be president, vice president, secretary, and treasurer? Is this
a combination or a permutation? Explain.
Part B: Next, 2 of the remaining 6 candidates are chosen to be the at-large board
members. In how many ways can they be chosen? Is this a combination or a
permutation? Explain.
Part C: The chorus decides to choose the 2 at-large board members from the 6
remaining candidates randomly. What is a fair way to do this?
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