Use the Pigeonhole Principle for the following problems: da) Lemurs are being assigned to 8 different exhibits spread throughout your zoo. What is the smallest number of lemurs necessary in order to guarantee that at least 4 lemurs are placed in some exhibit, no matter how they are assigned? Briefly justify your answer. (b) You have 87 zebrafish at your zoo, and they each have a number of stripes that is at least 1 and at most 9. If we used the pigeonhole principle, what property can we guarantee about our zebrafish? (c) Your zoo gets inhabited by rats. Upon inspection, you find that there are 67 rats spread over 4 nests. We know that the largest nest is at least how big? Briefly describe how you arrived at your answer.

Use the Pigeonhole Principle for the following problems: da) Lemurs are being assigned to 8 different exhibits spread throughout your zoo. What is the smallest number of lemurs necessary in order to guarantee that at least 4 lemurs are placed in some exhibit, no matter how they are assigned? Briefly justify your answer. (b) You have 87 zebrafish at your zoo, and they each have a number of stripes that is at least 1 and at most 9. If we used the pigeonhole principle, what property can we guarantee about our zebrafish? (c) Your zoo gets inhabited by rats. Upon inspection, you find that there are 67 rats spread over 4 nests. We know that the largest nest is at least how big? Briefly describe how you arrived at your answer.

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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2. If there are 120 people in your college class, are there at least 5 people that share the same last initial? a. Let the pigeon holes be: b. Let the pigeons be: c. What is k? d. Now the number of pigeons would have to be greater than: e. Is the number of pigeons or people greater? Why or why not? f. Are there at least 5 people that share the same last initial if there are 120 people in the college class? Why or why not? Write your response below: