Question 329240: I am walking a group of 6 dogs. In how many different orders can the dogs enter my house in single file.
thank you for your help. Answer by solver91311(24713) (Show Source):
6 ways to choose the first dog. For each of those 6 ways, there are 5 ways to choose the second dog, making a total of 30 ways so far. Then for each of those 30 ways, there are 4 ways to choose the third dog...and so on, until you run out of dogs.
Mathematicians, being the exceedingly lazy lot we are, have a shorthand for this
