2018 AMC 8 Problem 16
Attempt Problem 16 of the 2018 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2018 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
16.
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: C
Small hint:
Treat the two Arabic books as one block and the four Spanish books as one block.
Big hint:
Arrange the five objects, then arrange the books within the Arabic and Spanish blocks.
Video solution:
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Written solution:
Since we are keeping the Arabic books together and the Spanish books together, we can look at each group as a single block.
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 together, there are ways of ordering the Arabic books and ways of ordering the Spanish books. Therefore, the total ways to order the books is
Thus, the correct answer is C.
Problem 16 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
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