Problem 3. How many ways are there to select an 11-member soccer team and a 5-memberbasketball team from a class of 30 students if(1) nobody can be on both teams.(2) any number of students can be on both the teams.(3) at most one student can be on both the teams.

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Answered: Problem 3. How many ways are there to…

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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Suppose that Jeremy is a highschool science teacher and that he is dividing 16 students in his advanced chemistry class into four groups of four for a lab activity. Each of the four lab groups has been assigned its own task to complete for the activity, but the students are not assigned specific roles within the group. How many different ways can Jeremy assign his students to the four lab groups?
Consider a 6 vs 6 youth soccer team (i.e., teams field 6 players at once) with 9 players. (a) How many different combinations of players can the team field? (b) If the team has exactly one goalie (who has to play), how many different combinations of players can the team field? (c) If the team has exactly two goalie (exactly one of which has to play and the other cannot), how many different combinations of players can the team field?
If there are four (4) students namely: Sonia, Yumi, Rin, and Eggy. How many different seating arrangements in a bench can be made considering all the students at a time, if Sonia must always be first and Eggy can never be last?
2.) The BOS-14 is the new model of cars manufactured by NUC Motors. This model can be achieved in 2 body styles, 4 interior options and 7 different colors. The model can be achieved in automatic transmission as a manual. ER Auto wants to have a model of each of the options available to sell. How many BOS-14 models should you order?
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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?
PART IV. Solve the following problems. You have eight books and are going to put four on a bookshelf. How many different ways can the books be ordered on the bookshelf? 1. You have seven books and are going to randomly select three to read. How many different combinations of books might you select?
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For this problem, assume the cooler contains 28 cans, 10 of which are regular, and the rest of which are diet. (1) How many ways can you choose 5 cans from the cooler? (2) How many ways can you choose 5 regular cans from the cooler? (3) How many ways can you choose 5 diet cans from the cooler? (4) How many ways can you choose 5 cans from the cooler so that at least 4 are diet?

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Problem 3. How many ways are there to select an 11-member soccer team and a 5-member basketball team from a class of 30 students if (1) nobody can be on both teams. (2) any number of students can be on both the teams. (3) at most one student can be on both the teams.