Question

将 $1$ 块棕色砖、 $1$ 块紫色砖、 $2$ 块绿色砖和 $3$ 块黄色砖从左到右排成一行，有多少种可区分的排列？同色砖不可区分。

How many distinguishable arrangements are there of $1$ brown tile, $1$ purple tile, $2$ green tiles, and $3$ yellow tiles in a row from left to right? (Tiles of the same color are indistinguishable.)

$210$

$420$

$630$

$840$

$1050$

答案：B

知识点：多重集排列

难度评级：900

解答：

砖块总数为 $1+1+2+3=7$ 。若七块都不同有 $7!$ 种排列。两块绿色砖不可区分，三块黄色砖不可区分，所以要除以 $2!$ 和 $3!$ 。

因此可区分的排列数为 $\frac{7!}{2!3!}=420.$

所以正确答案是 B。

There are $1+1+2+3=7$ total tiles. If all seven tiles were distinct, there would be $7!$ arrangements. The two green tiles are indistinguishable, and the three yellow tiles are indistinguishable, so we divide by $2!$ and $3!.$

Thus the number of arrangements is $\frac{7!}{2!3!}=420.$

Thus, B is the correct answer.

2020 AMC 10B 第 5 题

答案：B

难度评级：900

解答：

其他年份的第 5 题