Question

Suppose there are five main roads between the cities A and B. In how many ways can a man go from a city to the other and return by a different road?

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Answer 1

Answer:

There are 240 ways can a person drive from A to C and return, going through B on both trips without driving on the same road twice is

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Answer 2

Given: Number of roads between the cities A and B = 5

To find: Number of ways a man can go from a city to the other and return by a different road

Solution: Here we have to apply the rules of permutation.

A permutation is an arrangement of all or part of a set of objects, with regard to the order of the arrangement.

Since there are five roads available to travel by, the man go from A to B in 5 different ways.

As he needs to take a different road for returning, he can return by 4 (5 - 1) ways.

Therefore, the number of different ways in which the man can go from a city to the other and return by a different road = 5 × 4 = 20

Answer: 20