Page Turner loves discrete mathematics. She has 8 graph theory books, 6 books about combinatorics and 4 set theory books. Thus, in total there are 8 + 6 + 4 = 18 books. The arrangement of books can be obtained by using concept of permutations. a) Arranging a book in such a way that there are no restrictions can be: 8 + 6 + 4 = 18! b) Condition for graph theory book is: graph theory books are next to each other but the others could be anywhere on the shelf. 1 + 6 + 4= 11! Thus, arrangement of the book will be: 8! (11!) c) books are organized by their topic, there will be permutations amongst books as there are 8 graph theory books, 6 books about combinatorics and 4 set theory books and types of books are 3: The finnaly answer is: 8! 6! 4! 3!