2018 AMC 8 Problems/Problem 16
Contents
Problem 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?
Video Solution
Solution
Since the Arabic books and Spanish books have to be kept together, we can treat them both as just one book. That means we're trying to find the number of ways you can arrange one Arabic book, one Spanish book, and three German books, which is just factorial. Now we multiply this product by
because there are
factorial ways to arrange just the Arabic books, and
ways to arrange just the Spanish books. Multiplying all these together, we have
See Also
2018 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 15 |
Followed by Problem 17 | |
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