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Chapter 4: Problem 27

A businessman in New York is preparing an itinerary for a visit to six major cities. The distance traveled, and hence the cost of the trip, will depend on the order in which he plans his route. How many different itineraries (and trip costs) are possible?

Short Answer

Expert verified
Answer: The businessman has 720 different possible itineraries for visiting the six major cities.

Step by step solution

01

Find out how many cities the businessman needs to visit

The businessman needs to visit six major cities.
02

Understand that we need to find the number of possible itineraries

We are asked to find the number of different itineraries (and trip costs) that are possible. Since the order of visiting the cities matters, we will use permutations to find the answer.
03

Calculate the number of possible itineraries using permutation

The businessman can visit the first city in 6 different ways (as there are 6 cities to choose from). After visiting the first city, he has 5 remaining cities to visit for the second city. For the third city, he has 4 remaining choices, and so on. Therefore, the total number of possible itineraries can be calculated as: 6 脳 5 脳 4 脳 3 脳 2 脳 1 = 720 itineraries.
04

Final answer

The businessman has 720 different possible itineraries (and trip costs) for visiting the six major cities.

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