Answer the question in Example 8.10 for the case of six villages. Example 8.10 In a certain

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Answer the question in Example 8.10 for the case of six villages.
Example 8.10
In a certain area of the countryside are five villages. An engineer is to devise a system of two-way roads so that after the system is completed, no village will be isolated. In how many ways can he do this?
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