Question

A truck driver has to deliver bread to 9 grocery stores. The stores are located in 2 towns far enough apart that the driver wants to make all stops in 1 town before going onto the next. In how many different ways can he schedule the order of his stops if the larger town has 5 stores?

Answer 1

In the town with 5 stores, there will be a number of ways, call it "x", that show the number of ways to select the order of stops. Same for the town with 4 stores, but we call this "y". The driver will not go "back-and-forth", but finish out a town and then go to the next, so the total number of ways will be x times y. For "x", any of the stores could be the first stop, so there are 5 ways to select the first store in that town, multiplied by any of the 4 that are left, multiplied by any of the 3 that are left, etc. Similar for getting "y", from the town that has 4 stops.

Answer 2

Now, once you have x times y, the end answer will be 2xy because it is not stated which town he starts with. Really could be either town.