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.
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E.
Solution:
There are two ways to arrange the two Arabic books among themselves and there are ways to arrange the four Spanish books among themselves. If the two Arabic books are considered as a unit and the four Spanish books are considered as a unit, then, including the three German books, there are five objects to arrange on the shelf. These five objects can be arranged on the shelf in ways. So altogether the books can be arranged in ways.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions