AMC 8 2008 Problem 14

AMC8 2008 年第 14 题

排列与组合★★★☆☆
Three A’s\text{A's}, three B’s\text{B's}, and three C’s\text{C's} are placed in the nine spaces so that each row and column contain one of each letter. If A\text{A} is placed in the upper left corner, how many arrangements are possible?
把三个 A,三个 B 和三个 C 放置在九个空格中,使得每行和每列包含三个字母中的每一个字母。 如果 A 放置在左上角,那么一共有多少种安排方法?
AMC 8 2008 Problem 14 figure
  1. A.2
  2. B.3
  3. C.4
  4. D.5
  5. E.6

正确答案 · Correct Answer

C

解析 · Solution

Solution 1

Solution There are 2 ways to place the remaining As\text{As}, 2 ways to place the remaining Bs\text{Bs}, and 1 way to place the remaining Cs\text{Cs} for a total of (2)(2)(1) = 4.

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