2018 AMC 8 第 16 题
先试着解答 2018 AMC 8 第 16 题，然后核对你的答案与视频与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2018 AMC 8 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
16.
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?
小提示：
把两本阿拉伯语书看成一个整体，把四本西班牙语书看成一个整体
Treat the two Arabic books as one block and the four Spanish books as one block.
大提示：
先排列五个对象，再排列阿拉伯语块和西班牙语块内部的书
Arrange the five objects, then arrange the books within the Arabic and Spanish blocks.
视频讲解：
Click to load, then click again to play
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 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 种方式排列这 个对象。阿拉伯语书块内部有 种排列，西班牙语书块内部有 种排列，所以总排列数为
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 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.
其他年份的第 16 题
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
- 1995 AMC 8
- 1996 AMC 8
- 1997 AMC 8
- 1998 AMC 8
- 1999 AMC 8
- 2000 AMC 8
- 2001 AMC 8
- 2002 AMC 8
- 2003 AMC 8
- 2004 AMC 8
- 2005 AMC 8
- 2006 AMC 8
- 2007 AMC 8
- 2008 AMC 8
- 2009 AMC 8
- 2010 AMC 8
- 2011 AMC 8
- 2012 AMC 8
- 2013 AMC 8
- 2014 AMC 8
- 2015 AMC 8
- 2016 AMC 8
- 2017 AMC 8
- 2019 AMC 8
- 2020 AMC 8
- 2022 AMC 8
- 2023 AMC 8
- 2024 AMC 8
- 2025 AMC 8
- 2026 AMC 8