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Olympiad workbookIOQMPermutation and Combination

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.)

Correct answer

60

Step-by-step solution

aligned & ways = ^4 C₂ 2!+ ^4 C₃ 3!+ ^4 C₄ 4! & =12+24+24=12+48=60 aligned

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