Suppose a company needs temporary passwords for the trial of a new time management software. Each password will have one digit, followed by one letter, followed by two digits. The digit 7 will not be used. So, there are 26 letters and 9 digits that will be used. Assume that the digits can be repeated. How many passwords can be created using this format?
Question
Suppose a company needs temporary passwords for the trial of a new time management software. Each password will have one digit, followed by one letter, followed by two digits. The digit 7 will not be used. So, there are 26 letters and 9 digits that will be used. Assume that the digits can be repeated. How many passwords can be created using this format?
Solution
To solve this problem, we need to use the counting principle, which states that if there are n ways to do one thing, and m ways to do another, then there are n*m ways of doing both.
- For the first digit, we have 9 choices (0-6, 8-9) because we can't use 7.
- For the letter, we have 26 choices (A-Z).
- For the third character, which is a digit, we again have 9 choices.
- For the fourth character, which is also a digit, we again have 9 choices.
So, the total number of passwords is 9 * 26 * 9 * 9 = 18954.
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