在 Mathland 这个小国家，所有汽车的牌照都有 4 个符号。第一个符号必须是个韵母（$A$, $E$, $I$, $O$ 或 $U$），第二个和第三个符号必须是 21 个非韵母中不同的两个字母，第四个必须是一个数字（0 到 9），如果符号都是按照这些规则随机选择的，那么牌照上显示的是 "$AMC8$" 概率是多少？

A. $\frac{1}{22050}$

B. $\frac{1}{21000}$

C. $\frac{1}{10500}$

D. $\frac{1}{2100}$

E. $\frac{1}{1050}$

1. 2015 AMC 8 官方解析

There is one favorable case, which is the license plate that says "$AMC8$." We must now find how many total cases there are. There are 5 choices for the first letter (since it must be a vowel), 21 choices for the second letter (since it must be of 21 consonants), 20 choices for the third letter (since it must differ from the second letter), and 10 choices for the number. This leads to $5 \cdot 21 \cdot 20 \cdot 10 = 21000$ total possible license plates. That means the probability of a license plate saying "$AMC8$" is $\frac{1}{21000}$.