A server generates random passwords of 3 letters followed by 3 digits. How many different passwords are possible if letters and digits can be repeated? Choose the correct choice from the following options
A) 26 × 3 × 10 × 4 B) 26³ x 1000 C) 26³ × 10 000 × 9 × 9 × 9 × 9 D) 26 × 25 × 24 × 10 000 E) 26 × 25 × 24 x 23 x 21 x 20
OFFICIAL SOLUTION:   (B) The formula for permutations of events is the product of the number of ways each event can occur. There are 26 letters and 10 digits. So there are 26 × 26 × 26 options for the three letters, and 10 × 10 × 10 for the three digits. The number of passwords generated is 26 × 26 × 26 × 10 × 10 × 10 = 26³ × 1000.   The correct answer is choice (26³ x 1000).
<result>B</result>
A server generates random passwords of 3 letters followed by 3 digits. How many different passwords are possible if letters and digits can be repeated?