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?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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).
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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