AMC 8 2018 Problem 16
AMC8 2018 年第 16 题
排列与组合★★★☆☆
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?
教授有 9 本不同的书在书架上排成一排：2 本阿拉伯语书，3 本德语书和 4 本西班牙语书。有多少种把这些书排成一排的方式，要求阿拉伯语书在一起，并且西班牙语书也要在一起？
- A.1440
- B.2880
- C.5760
- D.182,440
- E.362,880
正确答案 · Correct Answer
C
解析 · Solution
Solution 1
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. So now we try to find the german book possibilities, (Arabic block), (Spanish block), German book 1, German book 2, German book 3. 5! Multiplying all these possibilities(2!,4!,5!) gives the total number of arrangements which is 5760. ways to arrange the nine books while keeping the Arabic and Spanish books together. -TORPEDOROCKS
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