Question

Chang 教授有九本不同的语言书排在书架上：两本阿拉伯语书、三本德语书和四本西班牙语书。若要求阿拉伯语书放在一起，西班牙语书也放在一起，那么这九本书有多少种排列方式？

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?

$1440$

$2880$

$5760$

$182,440$

$362,880$

答案：C

知识点：排列有限制的排列

难度评级：1100

视频讲解：

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文字解答：

把两本阿拉伯语书作为一个块，四本西班牙语书作为一个块。

此时共有 $5$ 个对象：三本德语书、一个阿拉伯语书块、一个西班牙语书块，可用 $5!$ 种方式排列。阿拉伯语书块内部有 $2!$ 种排列，西班牙语书块内部有 $4!$ 种排列，所以总排列数为 $\begin{align*}5! \cdot 4! \cdot 2! &= 120 \cdot 24 \cdot 2 \\&= 5760 \end{align*}$

所以正确答案是 C。

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 5 objects on the bookshelf: three German books, one collection of Arabic books, and one collection of Spanish books. There are $5!$ ways to order the $5$ objects. As we already have the books together, there are $2!$ ways of ordering the Arabic books and $4!$ ways of ordering the Spanish books. Therefore, the total ways to order the books is $\begin{align*}5! \cdot 4! \cdot 2! &= 120 \cdot 24 \cdot 2 \\&= 5760 \end{align*}$

Thus, the correct answer is C.

2018 AMC 8 第 16 题

答案：C

难度评级：1100

视频讲解：

文字解答：

其他年份的第 16 题