Questions: 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?

Solution Steps

To determine the number of possible passwords, we need to calculate the number of ways to choose each part of the password and then multiply these numbers together. Since each password consists of two digits followed by two letters, and given the constraints, we can break it down as follows:

1. Calculate the number of choices for each digit.
2. Calculate the number of choices for each letter.
3. Multiply the number of choices for the digits and letters together to get the total number of possible passwords.

The available digits are \(0, 1, 2, 4, 5, 7, 8, 9\), which gives us a total of \(8\) digits. Each password requires \(2\) digits, and since digits can be repeated, the number of combinations for the digits is given by: \[ \text{Choices for digits} = 8^2 = 64 \]

The available letters are all letters from \(A\) to \(Z\) excluding \(J, K, L\). This results in \(26 - 3 = 23\) letters. Each password requires \(2\) letters, and since letters can also be repeated, the number of combinations for the letters is: \[ \text{Choices for letters} = 23^2 = 529 \]

To find the total number of possible passwords, we multiply the number of choices for the digits by the number of choices for the letters: \[ \text{Total passwords} = \text{Choices for digits} \times \text{Choices for letters} = 64 \times 529 = 33856 \]

Final Answer