Suppose a company needs temporary passwords for the trial of a new time management software. Each password will have two letters followed by two digits. The digits 7,8 , and 9 will not be used. So, there are 26 letters and 7 digits that will be used. Assume that the letters and digits can be repeated. How many passwords can be created using this format? passwords

To create a password with the format of two letters followed by two digits, we can break it down into parts. For the letters, there are 26 options available (A-Z), and since repetition is allowed, each of the two letter positions can also have 26 choices. So, for the letters, we calculate it as \( 26 \times 26 \). For the digits, since only 0-6 are allowed (7 total digit options), and again repetition is allowed, the calculation for the digits will be \( 7 \times 7 \). Combining both parts, the total number of possible passwords turns out to be: \[ (26 \times 26) \times (7 \times 7) = 676 \times 49 = 33,124. \] So, a grand total of **33,124 unique passwords** can be created!