Suppose that a sales person has to visit eight different cities including London. They must begin their trip in London, but can visit the other seven cities in any order they wish. How many possible orders can the sales person use when visiting these cities?

Question

Colt Hobbs

Business

12 May, 07:59

Suppose that a sales person has to visit eight different cities including London. They must begin their trip in London, but can visit the other seven cities in any order they wish. How many possible orders can the sales person use when visiting these cities?

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Answers (1)

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Ralph Price · Answer 1

The possible orders can the sales person use when visiting the cities are:

5040

Explanation:

The number of orders in which sellers can visit seven cities can be calculated by identifying the number of possibilities, therefore it can be said:

There are 7 cities to visit in the beginning, therefore that is the number of possibilities to visit in the first place (after London of course), however, for the second city to visit there are no longer the seven initial options but reduce by one, and so on by continuing to select cities until at the end there is only one option to choose, therefore the number of possible orders would be calculated:

7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040

This result can also be calculated using the factorial (!) Which is the number of ways in which a certain number of objects can be organized, which would have:

7! = 5040