2. 外语
  3. Suppose that a computer password consists of four characters such that the first character is one of the 10 digits from 0 to 9 a

Suppose that a computer password consists of four characters such that the first character is one of the 10 digits from 0 to 9 a

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问题 Suppose that a computer password consists of four characters such that the first character is one of the 10 digits from 0 to 9 and each of the next 3 characters is any one of the uppercase letters from the 26 letters of the English alphabet. How many different passwords are possible?
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答案156,000
解析 The description of the password allows repetitions of letters. Thus, there are 10 possible choices for the first character in the password and 26 possible choices for each of the next 3 characters in the password. Therefore, applying the multiplication principle, the number of possible passwords is(10)(26)(26)(26)= 175,760.
Note that if repetitions of letters are not allowed in the password, then the choices are not all independent, but a modification of the multiplication principle can still be applied. There are 10 possible choices for the first character in the password, 26 possible choices for the second character, 25 for the third character because the first letter cannot be repeated, and 24 for the fourth character because the first two letters cannot be repeated. Therefore, the number of possible passwords is(10)(26)(25)(24)= 156,000.
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