11:09 webwork.smith.edu .oooo AT&T; @* 11% XC review 1: Problem 5 Previous Probl

Question

11:09 webwork.smith.edu .oooo AT&T; @* 11% XC review 1: Problem 5 Previous Problem List Next (1 point) Page Turner loves discrete mathematics. She has 7 "graph theory" books, 4 books about combinatorics, and 6 "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. 16 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). Note: You can earn partial credit on this problem. Preview My Answers Submit Answers You have attempted this problem 1 time.

Explanation / Answer

Answers:

(a) 17!

(b) 11! 7!

(c) 3! 7! 4! 6!

EXPLANATION:

(a) Graph Theory books = 7

   Combinatorics          = 4

set theory books        = 6

Total                      = 17

17 books can be arraned in 17! ways

(b) First bundle the 7 graph theory books and consider that bundle as 1 book.

So, Total number of books = 11 books.

These 11 books can be arraged n 11! waya.

Now, 7 graph theory boks can be arranged in 7! ways.

So,

Total number of ways with graph theory books together = 11! 7! ways

(c) Bondle each topics books and consider each bundle as 1 book.

So, 3 bundles can be aranged in 3! ways.

Graph theory books can be arraged in 7! ways.

Combinatorials can be arranged in 4! ays.

set theoery can be arranged in 6! ways.

So,

Total number of rrangements:

3! 7! 4! 6!

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.