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Excursions in Modern Mathematics: Pearson New International Edition | 8th Edition | ISBN: 9781292022048 | Authors: Peter Tannenbaum
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Consider a TSP with 11 vertices labeled A through K. (a) How many tours are of the form

Chapter 6, Problem 34

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QUESTION:

Consider a TSP with 11 vertices labeled A through K. (a) How many tours are of the form A, B, . . . , A? (Hint: The remaining nine letters can be rearranged in any sequence.) (b) How many tours are of the form C, . . . , K, C? (c) How many tours are of the form D, B, . . . , K, D?

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QUESTION:

Consider a TSP with 11 vertices labeled A through K. (a) How many tours are of the form A, B, . . . , A? (Hint: The remaining nine letters can be rearranged in any sequence.) (b) How many tours are of the form C, . . . , K, C? (c) How many tours are of the form D, B, . . . , K, D?

ANSWER:

Step 1 of 3

Let us consider a TSP with 11 vertices labelled A through K.

The total number of vertices is 11.

When we start a tour of the form A, B, …., A, we know the starting point A and the second point B.

So, the number of tours of this form is the number of arrangements of the remaining nine alphabets.

9 remaining alphabets can be arranged in  ways.

So, the number of tours of the form A, B…, A is .

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