The standard serial numbers for a temporary ID card in a institution are 2 letters followed by 5 digits. How many different ID cards are possible if letters and digits can be repeated?  Pick:
A) 26 × 3 × 10 × 4  B) 26 × 25 × 24 × 10 × 9 × 8 × 7  C) 26³ × 9 × 9 × 9 × 9  D) 26 × 25 × 24 × 10 000  E) 26 x 26 x 100 000
OFFICIAL SOLUTION:   (E) 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 options for the two letters, and 10 × 10 × 10 × 10 x 10 for the five digits. The number of different license plates is 26 × 26 × 10 × 10 × 10 × 10 x 10 = 26 x 26 × 100 000.   The correct answer is choice (26 x 26 x 100 000).
<result>E</result>
The standard serial numbers for a temporary ID card in a institution are 2 letters followed by 5 digits. How many different ID cards are possible if letters and digits can be repeated?