There are 4 routes from home to a center and 6 routes from the center to a library. On the return trip, the route used on each stage of the outward trip cannot be reused in reverse. How many round trips are possible?

Correct answer: 360 ways

For the outward trip there are 4 × 6 choices. On the return, there are 5 choices from the library to the center (excluding the route just used) and 3 from the center to home. Thus there are 4 × 6 × 5 × 3 = 360 round trips.