omputer programming team has 9 members. )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 126 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 60 (i) 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 200 (i) 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? to a similar vway 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 8, 8 and not A, and neither A nor B leads to the conclusion that the total pumber 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 87 How many groups contain neither A nor 87
omputer programming team has 9 members. )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 126 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 60 (i) 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 200 (i) 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? to a similar vway 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 8, 8 and not A, and neither A nor B leads to the conclusion that the total pumber 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 87 How many groups contain neither A nor 87
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please help me with the last three questions!
Transcribed Image Text: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 126
(b) Suppose five team members are women and four are men.
(i) 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 60
(i) 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 280
(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 8, 8 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.s.s, 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 8?
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