A sales representative must visit nine cities. There are direct air connections between each of the cities. Use the multiplication rule of counting to determine the number of different choices the sales representative has for the order in which to visit the cities.

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Mathematics

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24 October, 01:48

A sales representative must visit nine cities. There are direct air connections between each of the cities. Use the multiplication rule of counting to determine the number of different choices the sales representative has for the order in which to visit the cities.

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Jamie Kirby · Answer 1

362880

Step-by-step explanation:

Given that a sales representative must visit nine cities. There are direct air connections between each of the cities

Since there are direct connections between any two pairs the sales rep can visit in any order as he wishes.

He has 9 ways to select first city, now remaining cities are 8. He can visit any one in 8 ways.

i. e. No of ways of visiting 9 cities in any order = 9P9

= 9!

= 362880

So no of ways he visits the cities since there are direct connections between any two cities is

362880