Answer:
The number of ways is  [tex]\left 9}\atop } \right. P _5 = 15120[/tex]
Step-by-step explanation:
From the question we are told that
  The number of factories visited is  [tex]n = 9[/tex]
  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
     [tex]\left 9}\atop } \right. P _5 = \frac{9!}{(9-5)!}[/tex]
Where P represents  permutation
 =>  [tex]\left 9}\atop } \right. P _5 = \frac{9 \ !}{4\ !}[/tex]
 =>   [tex]\left 9}\atop } \right. P _5 = \frac{9 *8*7 * 6 * 5 * 4!}{4\ !}[/tex]
=> Â Â [tex]\left 9}\atop } \right. P _5 = 15120[/tex]
