Suppose a company needs temporary passwords for the trial of a new payroll software. Each password will have two digits followed by two letters. The letters J, K, and L and the digits 3 and 6 will not be used. So, there are 23 letters and 8 digits that will be used. Assume that the letters and digits can be repeated. How many passwords can be created using this format?passwords
Question
Suppose a company needs temporary passwords for the trial of a new payroll software. Each password will have two digits followed by two letters. The letters J, K, and L and the digits 3 and 6 will not be used. So, there are 23 letters and 8 digits that will be used. Assume that the letters and digits can be repeated. How many passwords can be created using this format?passwords
Solution
To solve this problem, we need to understand that each position in the password can be filled independently.
- For the first position, we have 8 choices (digits from 0-9, excluding 3 and 6).
- For the second position, we also have 8 choices (the same digits can be repeated).
- For the third position, we have 23 choices (letters from A-Z, excluding J, K, and L).
- For the fourth position, we also have 23 choices (the same letters can be repeated).
Since each position is filled independently, we multiply the number of choices for each position together to get the total number of possible passwords.
So, the total number of passwords is 8 * 8 * 23 * 23 = 33,632 passwords.
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