A night watchman must check in at 9 stations in a warehouse during each round of inspection. He decides to try all possible sequences of the 9 stations and use the shortest of these as his routine round of inspection. There are 9! possible different sequences of the stations.
a. Why are there 9! different sequences?
b. How many sequences must he try?
c. If he walks 4 rounds of inspection each night, how many nights will he require to try all possible sequences?