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College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Counting And Probability

Section9.1: Counting

Problem 1E: The Fundamental Counting Principle says that if one event can occur in m ways and a second event can...

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There are 10 applicants for three sales positions at a department store. All of the applicants are qualified. In how many ways can the department store fill the three positions?
The Fundamental Counting Principle says that if one event can occur in m ways and a second event can in n ways, then the two events can occur in order in _______ X____ways. So if you have two choices for shoes and three choices for hats, then the number of different shoe-hat combinations you can wear is _______X______=_______.
A board of directors consisting of eight members is to chosen from a pool of 30 candidates. The board is to have a chairman, a treasurer, a secretary, and five other members. In how many ways can the board of directors be chosen?
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Due to a miscommunication, Ananya’s, Sara’s, and Irvane’s post-recitation parties all fall on the same day. Unfortunately, many of their friends are very popular and may have received several invites. Fortunately, Ananya, Sara, and Irvane are also quite popular, so in total, there are 5217 people invited to the three parties! Out of these people, 3152 were invited by Ananya, 1989 were invited by Sara, and 1622 were invited by Irvane. Additionally, 818 people were invited by both Ananya and Sara, 589 people were invited by both Ananya and Irvane, and 110 people were invited to all three events. How many people were invited by both Sara and Irvane?
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At Southwestern Oregon Community College, a committee is being formed to decide on what kinds of facilities the new Health and Sciences building will include.Many of the campus community want a say in this matter, and 1515 members consisting of faculty, staff, administration, and student government have indicated that they would like to be a part of this committee. However, there are only 55 spots on the committee.Of the 1515 members of the campus community who want to be a part of this committee, 1010 are women and 55 are men.To decide who gets to serve on this committee, the 1515 names will be put into a hat, mixed up, and 55 will be drawn at random.(a) What kind of probability distribution models the probability of that kk women are on the committee?(b) What values can kk possibly be?(c) Write the formula for the probability distribution function for the probability that kk women will serve on the committee.(d) What is the probability that this committee consists only of women?(e)…
At Southwestern Oregon Community College, a committee is being formed to decide on what kinds of facilities the new Health and Sciences building will include.Many of the campus community want a say in this matter, and 1515 members consisting of faculty, staff, administration, and student government have indicated that they would like to be a part of this committee. However, there are only 55 spots on the committee.Of the 1515 members of the campus community who want to be a part of this committee, 1010 are women and 55 are men.To decide who gets to serve on this committee, the 1515 names will be put into a hat, mixed up, and 55 will be drawn at random.(d) What is the probability that this committee consists only of women?(e) What is the probability that this committee consists only of men?

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