Question

The Environmental Protection Agency must visit nine factories for complaints of air pollution. In how many ways can a representative visit five of these to investigate this week? Since the representative's travel to visit the factories includes air travel, rental cars, etc., then the order of the visits will make a difference to the travel costs.

Answer 1

The number of ways is
`\left 9}\atop } \right. P _5 = 15120`

Explanation:

From the question we are told that

The number of factories visited is
`n = 9`

The number of factories to be visited by a representative r = 5

The number of way to visit the 5 factories is mathematically represented as

`\left 9}\atop } \right. P _5 = (9!)/((9-5)!)`

Where P represents permutation

=>
`\left 9}\atop } \right. P _5 = (9 \ !)/(4\ !)`

=>
`\left 9}\atop } \right. P _5 = (9 *8*7 * 6 * 5 * 4!)/(4\ !)`

=>
`\left 9}\atop } \right. P _5 = 15120`