I have stumbled across this problem on my mathematics book, the problem states:
A person is distributing 3 packages in a city consisting of 3 houses, each package assigned to a single house. He has lost the delivery notes, and doesn't know which package belongs to which house. What is the chance that at least a single package makes its way to the correct location if he distributes them randomly?
To solve the problem I decided to draw a simple "state machine". I assume that the order of visiting the houses doesn't change the result (am I wrong here?). The number below each package (the stars) is the house it's meant to be delivered to.
Clearly, 4 out of the 6 final states have at least one correctly distributed package, so 2/3 is the result.
The solution stated by the book is 0.704 (it's rounded).
After puzzling for some time, I decided to code a quick simulation in C++, and the simulation (assuming the same premises as these used to build the graphic) converges to 2/3, too, so I wonder, am I interpreting the problem correctly? What method can lead to the result given in the book? I assume I'm missing a very easy and straightforward method as this book is designed for students new to statistics.