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There are five cities A, B, C, D, E on a certain island. Each city is connected to every other city by road. In how many ways can a person starting from city A come back to A after visiting some cities without visiting a city more than once and without taking the same road more than once? (The order in which he visits the cities also matters : e.g., the routes A → B → C → A and A → C → B → A are different)
There are five cities A, B, C, D, E on a certain island. Each city is connected to every other city by road. In how many ways can a person starting from city A come back to A after visiting some cities without visiting a city more than once and without taking the same road more than once? (The order in which he visits the cities also matters : e.g., the routes A → B → C → A and A → C → B → A are different)
He can visit all 4 cities or 3 cities or 2 cities from B, C, D, E.
If he visits all 4 cities = 4! = 24
If he visits 3 cities = 4C3.3! = 24
If he visits 2 cities = 4C2.2! = 12
∴ Total ways = 60