2018 AMC 8
Complete problem set with solutions and individual problem pages
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?
- A.
- B.
- C.
- D.
- E.
To solve this, treat the two Arabic books as one unit and the four Spanish books as another unit. Along with the three German books, you now have five units to arrange.
You can arrange these five units in ways. Within the Arabic block, the two books can be arranged in ways, and within the Spanish block, the four books can be arranged in ways.
Multiplying all these possibilities gives the total number of arrangements which is ways to arrange the nine books while keeping the Arabic and Spanish books together.
