### Problem 7: Committee Selection in a Programming TeamA computer programming team has 15 members consisting of eight humans and seven robots. A committee of exactly 6 of these team members must be put together to work on bug testing. **You may leave your answers unreduced.**#### (a) How many committees can be chosen that contain exactly four humans and two robots?#### (b) How many committees can be chosen that contain at most one robot?#### (c) How many committees can be chosen that contain at least one human?---### Explanation:In this problem, we explore combinatorial selection of team members under given constraints. The solution involves understanding and applying the principles of combinations.1. **Part (a):** We need to determine the number of ways to form a committee with exactly 4 humans and 2 robots.2. **Part (b):** We need to count the number of possible committees that include at most one robot, which means considering committees with 0 or 1 robot.3. **Part (c):** We need to figure out the total number of committees containing at least one human.By breaking down these scenarios, we can effectively apply combinatorial mathematics to solve the problem.

7. Given that a computer programming team has 15 members consisting of 8 humans and 7 robots. Also,…

Answered: 7. A computer programming team has 15…

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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A company is organizing a team-building event with various activities. There are 12 employees attending the event, and they need to be split into three teams: Team A, Team B, and Team C. Each team should have at least 2 members but no more than 6 members. In how many different ways can the teams be formed? (Note: The order of the teams doesn't matter; i.e., Team A, Team B, and Team C is the same as Team C, Team A, and Team B.)
A bagel shop has a selection of 8 different kinds of bagels (at least 10 of each). (.1) How many different selections of 10 bagels can be made? ( .2) If garlic is one kind of available bagel and onion is another, how many different selections of 10 bagels can you make so that you have at least 3 onion bagels and exactly 2 garlic bagels?
A computer programming team has 15 members consisting of eight robots and seven humans. A committee of exactly 7 of these team members must be put together to work on bug testing. You may leave your answer unreduced. (a)How many committees can be chosen that contain exactly four robots and three humans? (b) How many committees can be chosen that contain at most two robots? (c) How many committees can be chosen that contain at least one human?
Company C has 20 employees who are available to serve on a new committee. If the committee will consist of six members at large, the number of different possible committees is __________.
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Suppose we want to choose 4 objects, without replacement, from 17 distinct objects. (a) If the order of the choices is not relevant, how many ways can this be done? (b) If the order of the choices is relevant, how many ways can this be done?
It’s the first day of summer camp, and the counselors are trying to figure out where one of the campers will sleep. There are four beds available in Cabin #1, five in Cabin #2, and just one in Cabin #3. How many ways in all are there to assign the camper to a bed?
. Suppose you are working on a ten-digit keypad to open a door. You know the combination is exactly three digits long.1. How many choices are there if you may use a number multiple times and the order matters?2. How many choices are there if you may not use a number multiple times and the order matters?3. How many choices are there if you may not use a number multiple times and the order doesnot matter?4. How many choices are there if you may use a number multiple times and the order does notmatter?
A computer programming section has 11 members. A team of 5 is to be chosen to work on a special project. (a) How many ways can the team be chosen? (b) Suppose there are 6 men and 5 women in the section. How many teams of 5 have no women? How many teams of 5 have one woman ? How many teams of 5 have two women? How many teams of 5 have at most two women? (c) Two team members refuse to work together on projects. The teams must include one or neither of them. Now how many teams of 5 can be chosen to work on the project?
A computer programming team has 17 members. Suppose nine team members are women and eight are men. How many groups of nine can be chosen that contain at most three women? A group of nine that contains at most three women can contain no women, one woman, two women, or three women. So, the number of groups of nine that contain at most three women is? Suppose two team members refuse to work together on projects. How many groups of nine can be chosen to work on a project? Suppose two team members insist on either working together or not at all on projects. How many groups of nine can be chosen to work on a project?
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