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Consider a TSP with nine vertices labeled A through I. (a) How many tours are of the
Chapter 6, Problem 33(choose chapter or problem)
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?
Questions & Answers
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.).