AMC 8 2016 Problem 17
AMC8 2016 年第 17 题
基本计数原理★★★☆☆
An ATM password at Fred's Bank is composed of four digits from 0 to 9 , with repeated digits allowable. If no password may begin with the sequence 9,1,1, then how many passwords are possible?
Fred 银行的取款机密码由 0 到 9 中的 4 个数字组成，且允许重复，如果密码不允许以序列 9,1,1 开头，那么一共有多少种可能的密码？
- A.30
- B.7290
- C.9000
- D.9990
- E.9999
正确答案 · Correct Answer
D
解析 · Solution
Solution 1
For the first three digits, there are combinations since 911 is not allowed. For the final digit, any of the 10 numbers are allowed. .
Counting the prohibited cases, we find that there are 10 of them. This is because, when we start with 9,1, and 1, we can have any of the 10 digits for the last digit. So, our answer is
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