\(n\) people in a town own \(n\) different volumes of the encyclopedia in a specific manner. It is true that each resident owns \(k\) different volumes; in addition, each volume is owned by \(k\) different residents.
1. Show that for all \(n\) and \(k\), that there exists a distribution of the volumes that satisfy the requirements.
For example, person 1 can own Volumes 1 and 2, person 2 can own volumes 2 and 5, person 3 can own volumes 4 and 5, etc.
2. Find the total number of books in the town.
3. Find the number of different ways the residents can own the books.