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.

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Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.