Since the two Arabic books and four Spanish books have to be kept together, respectively, we can treat them both as just one book. That means we\textquotesingle re trying to find the number of ways you can arrange one Arabic book, one Spanish book, and three German books, which is just $\_5P\_5$. Now we multiply this product by $\_2P\_2\times \_4P\_4$~because there are $\_2P\_2$~ways to arrange just two Arabic books, and $\_4P\_4$~ways to arrange just four Spanish books. Multiplying all these together, we have the answer $C$. 
Professor Chang has nine language books lined up on a bookshelf: two different Arabic books, three different German books, and four different Spanish books. How many ways are there to arrange the nine books on the shelf keeping the Arabic books together and keeping the Spanish books together? ($2018$ AMC $8$ Problem, Question \#$16$)  $\textasciitilde$  $\textasciitilde$  $\textasciitilde$  \hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}$\textasciitilde$  \hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}$\textasciitilde$  \hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}$\textasciitilde$  \hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}$\textasciitilde$  \hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}$\textasciitilde$  \hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}$\textasciitilde$\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}  \hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}$\textasciitilde$  \hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}$\textasciitilde$ 
Options:
[1] $$1440$$ 
[2] $$2880$$ 
[3] $$5760$$ 
[4] $$182440$$ 
[5] $$362880$$ 