Consider a TSP with nine vertices labeled A through I. (a) How many tours are of the

Chapter 6, Problem 33

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QUESTION:

Consider a TSP with nine vertices labeled A through I. (a) How many tours are of the form A, G, . . . , A? (Hint: The remaining seven letters can be rearranged in any sequence.) (b) How many tours are of the form B, . . . , E, B? (c) How many tours are of the form A, D, . . . , F, A?

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QUESTION:

Consider a TSP with nine vertices labeled A through I. (a) How many tours are of the form A, G, . . . , A? (Hint: The remaining seven letters can be rearranged in any sequence.) (b) How many tours are of the form B, . . . , E, B? (c) How many tours are of the form A, D, . . . , F, A?

ANSWER:

Step 1 of 3

(a)

We have a tour whose starting vertex we know but we also know the second vertex in the tour. We still have seven other vertices we need to visit, this we can do in  ways (the third vertex is one of the seven vertices, the fourth is one of the  remaining vertices, etc.).

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