Problem:
Professor Chang has nine different language books lined up on a bookshelf: two Arabic, three German, and four Spanish. How many ways are there to arrange the nine books on the shelf keeping the Arabic books together and keeping the Spanish books together?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Since we are keeping the Arabic books together and the Spanish books together, we can treat each collection of books as a single object. As such, there are objects on the bookshelf: three German books, one collection of Arabic books, and one collection of Spanish books. There are ways to order the objects. As we already have the books grouped together, there are: ways of ordering the Arabic books, and ways of ordering the Spanish books. Therefore, the total number of ways to order the books is:
Thus, the correct answer is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions