Clever Counting Investigation 3. Making Rounds A. How many paths are there from A to B? How many...

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Clever Counting Clever Counting Investigation 3

Transcript of Clever Counting Investigation 3. Making Rounds A. How many paths are there from A to B? How many...

Page 1: Clever Counting Investigation 3. Making Rounds 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.

Clever CountingClever Counting

Investigation 3

Page 2: Clever Counting Investigation 3. Making Rounds 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.

• Making Rounds

Page 3: Clever Counting Investigation 3. Making Rounds 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.

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?

Page 4: Clever Counting Investigation 3. Making Rounds 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.

NetworkingNetworking• 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.

A B C

Edge

Path

Page 5: Clever Counting Investigation 3. Making Rounds 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.

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

Page 6: Clever Counting Investigation 3. Making Rounds 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.

1 x 8 = 8 paths

Page 7: Clever Counting Investigation 3. Making Rounds 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.

2 x 5 = 10 paths

Page 8: Clever Counting Investigation 3. Making Rounds 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.

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.

Page 9: Clever Counting Investigation 3. Making Rounds 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.

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

Page 10: Clever Counting Investigation 3. Making Rounds 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.