AMC8 2008
AMC8 2008 · Q14
AMC8 2008 · Q14. It mainly tests Basic counting (rules of product/sum), Casework.
Three As, three Bs and three Cs are placed in the nine spaces so that each row and column contain one of each letter. If A is placed in the upper left corner, how many arrangements are possible?
在九个空格中放置三个A、三个B和三个C，使得每行和每列包含每个字母各一个。如果A放在左上角，可能的排列有多少种？
(A)
2
2
(B)
3
3
(C)
4
4
(D)
5
5
(E)
6
6
Answer
Correct choice: (C)
正确答案：（C）
Solution
Answer (C): There are only two possible spaces for the B in row 1 and only two possible spaces for the A in row 2. Once these are placed, the entries in the remaining spaces are determined.
The four arrangements are:
答案（C）：第 1 行中 B 只有两个可能的位置，第 2 行中 A 也只有两个可能的位置。一旦把它们放好，其余空格中的条目就被确定了。
四种排列为：
Topics
Related Questions
Practice full AMC exams on amcdrill.
Try full-length practice and diagnostics at www.amcdrill.com.