A night watchman visits 8 offices every night. To prevent others from knowing when he will be at a particular office, he varies the order of his visits. In how many ways can this be done?
A) 20,160
B) 8
C) 1
D) 5,040
E) 40,320

Question

A night watchman visits 8 offices every night. To prevent others from knowing when he will be at a particular office, he varies the order of his visits. In how many ways can this be done?​ ​
A) ​20,160
B) ​8
C) ​1
D) ​5,040
E) ​40,320

Quizplus · Accepted Answer

The night watchman can visit the first office in 8 ways, the second office in 7 ways (as one office has already been visited), the third office in 6 ways, and so on until the eighth office which has only 1 way left. Hence, the total number of ways is 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320.

A Night Watchman Visits 8 Offices Every Night