# Page Turner loves discrete mathematics. She has 8 "graph theory" books, 6 books about combinatorics, and 4 "set theory" books. How many ways can she place her discrete mathematics books on the same shelf in a row if: a) there are no restrictions. b) graph theory books are next to each other but the others could be anywhere on the shelf. c) books are organized by their topic (same kinds are next to each other).

2 points) Page Turner loves discrete mathematics. She has 8 "graph theory" books, 6 books about combinatorics, and 4 "set theory" books.
How many ways can she place her discrete mathematics books on the same shelf in a row if:
a) there are no restrictions.
b) graph theory books are next to each other but the others could be anywhere on the shelf.
c) books are organized by their topic (same kinds are next to each other).

## Want to know more about Discrete math?

• Questions are typically answered in as fast as 30 minutes

### Plainmath recommends

• Get a detailed answer even on the hardest topics.
• Ask an expert for a step-by-step guidance to learn to do it yourself.

Dora
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!