2025 SJI P2 Q6

Seven distinct books, including two highlighted titles Arcadia and Beacon, are to be displayed in a bookstore window. If all seven are arranged in a single row, find the number of ways the books can be arranged so that

1. Beacon appears immediately on the right of Arcadia.[2]
2. Beacon appears in any position on the right of Arcadia.[2]

The bookstore owner decided instead to arrange all seven books in two shelves, one above the other, and each shelf must hold at least one book.

3. Find the number of ways the books can be arranged.[3]