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Suppose a company needs temporary passwords for the trial of a new payroll software. Each password will have two letters, followed by one digit, followed by one letter. The letter W will not be used. So, there are 25 letters and 10 digits that will be used. Assume that the letters 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 payroll software. Each password will have two letters, followed by one digit, followed by one letter. The letter W will not be used. So, there are 25 letters and 10 digits that will be used. Assume that the letters can be repeated. How many passwords can be created using this format?

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Solution

To calculate the total number of possible passwords, we need to multiply the number of possibilities for each character in the password.

  1. For the first two letters, since we have 25 letters and they can be repeated, we have 25 possibilities for each letter. So, for the first two letters, we have 25 * 25 = 625 possibilities.

  2. For the digit, we have 10 possibilities (0-9).

  3. For the last letter, we again have 25 possibilities.

So, the total number of possible passwords is 625 (for the first two letters) * 10 (for the digit) * 25 (for the last letter) = 156,250.

Therefore, the company can create 156,250 different passwords using this format.

This problem has been solved

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