Question

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)

Answer 1

Answer:

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

Answer 2

Answer:

THE ANSWER IS 60

HOPE IT HELPED...........................