Alice has a ten-day vacation from school, and she wants to spend some of it reading. Beside her favorite comfy chair is a selection of 30 books. She will read exactly one of these books each day, for a total of ten different books. She is planning out what she will read each day.
a) How many different ways can she decide which book to read on each day?
b) Suppose that three of the books form a trilogy, so Alice wants to either read all three of them, in that order (but not necessarily on consecutive days), or not read any of them. Now how many different ways can she decide which book to read on each day?
c) Suppose that ten of the books are fiction, ten are non-fiction, and ten are poetry, and Alice wants to read at least one book of each type. Now how many different ways can she decide which book to read on each day?