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Clever Counting Investigation 3

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Making Rounds

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A. How many paths are there from A to B? How many paths are there from B to C? B. How many paths are there from A to C through B? Explain your reasoning. C. If Rodney has a small locker, how many paths from A to C pass by his locker? D. If Rodney has a large locker, how many paths from A to C pass by his locker? E. If Rodney has a small locker, what is the probability that the guard will not pass his locker on one of her rounds? F. If Rodney has a large locker, what is the probability that the guard will not pass his locker on one of her rounds?

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Networking A, B, and C are nodes. A path from node A to node C consists of an edge from node A to node B followed by a edge from node B to node C. AB C Edge Path

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This network models the warehouse floor plan because it contains all the important information in a simplified form.

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1 x 8 = 8 paths

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2 x 5 = 10 paths

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For each edge that connects nodes A and B, there are 32 ways to complete the path to node C, for a total of 25 x 32 = 800 paths.

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You have found the number of paths through several networks. In problem 3.3, you will design networks that satisfy given constraints.

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