A computer programming team has 9 members. (a) How many ways can a group of five be chosen to work on a project? As in Example 9.5.4, since the set of people in a group is a subset of the set of people on the team, the answer is (b) Suppose five team members are women and four are men. (1) How many groups of five can be chosen that contain three women and two men? As in Example 9.5.7a, think of forming the group as a two-step process, where step 1 is to choose the women and step 2 is to choose the men. The answer is (ii) How many groups of five can be chosen that contain at least one man? As in Example 9.5.7b, consider the relationship between the set of groups that consist entirely of women and the set of groups with at least one man. This thinkin that the number of groups with at least on man is (iii) How many groups of five can be chosen that contain at most three women? A group of five that contains at most three women can contain no women, one woman, two women, or three women. So, the number of groups of five that conta (c) Suppose two team members refuse to work together on projects. How many groups of five can be chosen to work on a project? In a similar way as in Example 9.5.6, let A and B be the two team members who refuse to work together in a group. Thinking about the number of groups that contain 1 nor R leads to the conclusion that the total number of groups of that can be chosen to work on the project is
A computer programming team has 9 members. (a) How many ways can a group of five be chosen to work on a project? As in Example 9.5.4, since the set of people in a group is a subset of the set of people on the team, the answer is (b) Suppose five team members are women and four are men. (1) How many groups of five can be chosen that contain three women and two men? As in Example 9.5.7a, think of forming the group as a two-step process, where step 1 is to choose the women and step 2 is to choose the men. The answer is (ii) How many groups of five can be chosen that contain at least one man? As in Example 9.5.7b, consider the relationship between the set of groups that consist entirely of women and the set of groups with at least one man. This thinkin that the number of groups with at least on man is (iii) How many groups of five can be chosen that contain at most three women? A group of five that contains at most three women can contain no women, one woman, two women, or three women. So, the number of groups of five that conta (c) Suppose two team members refuse to work together on projects. How many groups of five can be chosen to work on a project? In a similar way as in Example 9.5.6, let A and B be the two team members who refuse to work together in a group. Thinking about the number of groups that contain 1 nor R leads to the conclusion that the total number of groups of that can be chosen to work on the project is
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:A computer programming team has 9 members.
(a) How many ways can a group of five be chosen to work on a project?
As in Example 9.5.4, since the set of people in a group is a subset of the set of people on the team, the answer is
(b) Suppose five team members are women and four are men.
(1) How many groups of five can be chosen that contain three women and two men?
As in Example 9.5.7a, think of forming the group as a two-step process, where step 1 is to choose the women and step 2 is to choose the men. The answer is
(ii) How many groups of five can be chosen that contain at least one man?
As in Example 9.5.7b, consider the relationship between the set of groups that consist entirely of women and the set of groups with at least one man. This thinking leads to the conclusion
that the number of groups with at least on man is
(iii) How many groups of five can be chosen that contain at most three women?
A group of five that contains at most three women can contain no women, one woman, two women, or three women. So, the number of groups of five that contain at most three women is
(c) Suppose two team members refuse to work together on projects. How many groups of five can be chosen to work on a project?
In a similar way as in Example 9.5.6, let A and B be the two team members who refuse to work together in a group. Thinking about the number of groups that contain A and not B, B and not A.
and neither A nor B leads to the conclusion that the total number of groups of that can be chosen to work on the project is
(d) Suppose two team members insist on either working together or not at all on projects. How many groups of five can be chosen to work on a project?
As in Example 9.5.5, let A and B be the two team members who insist on working in a group together or not at all. How many groups contain both A and B? How many groups contain neither A
nor B?
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