Erik Allen repairs photocopy machines. According to his schedule, he needs to visit 5 different offices today. How many ways can Erik visit these offices and return to his headquarters?
A. 120

B. 5

C. 20

D. 24

Question

Erik Allen repairs photocopy machines. According to his schedule, he needs to visit 5 different offices today. How many ways can Erik visit these offices and return to his headquarters? 
 A. 120  
 
 B. 5  
 
 C. 20  
 
 D. 24

mathmate · Answer

Assuming distance is not a consideration, then there are 5! ways to visit all 5 offices.

anonymous · Answer

thank you so much!1 i thought it was a trick question..1

mathmate · Answer

The reason for 5! is because he has 5 choices to visit the first, 4 left for the second, 3 left for the third, 2 left to do for the fourth, and only one choice for the last.
All these are independent choices, so we can multiply them together to get 5!