2018 AMC 8 Problems/Problem 16
Contents
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?
=Solution
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 5! ways. Within the Arabic block, the two books can be arranged in 2! ways, and within the Spanish block, the four books can be arranged in 4! ways.
Multiplying all these possibilities gives the total number of arrangements as:
.
This results in 5,760 ways to arrange the nine books while keeping the Arabic and Spanish books together.
Video Solution (CREATIVE ANALYSIS!!!)
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Video Solutions
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See Also
| 2018 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 15 |
Followed by Problem 17 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
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