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Page Turner loves discrete mathematics. She has 8 "graph theory" books, 5 books about combinatorics, and 7 "set theory" books. How many ways can she place her discrete mathematics books on the same shelf in a row if:

a.) I got it.

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).

a)

If the books can be placed in any order, there are a total of

books. The number of ways to arrange them in a row is given by the factorial of 20:

Therefore, there are approximately 2.43 × 10^18 ways to arrange Page Turner's discrete mathematics books on the shelf.

Refer Required solution