The standard model numbers of cell phones in a company are 1 letter followed by 6 digits. How many different model numbers are possible if letters and digits can be repeated?  Choose the most appropriate option:  A) 26 × 26 × 10 × 4  B) 26 x 100 000  C) 26 x 10  D) 26 × 25 × 24 × 10 × 9 × 8 × 7  E) 26 x 1 000 000
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 options for a letter, and 10 × 10 × 10 × 10 × 10 × 10 for the six digits. The number of different license plates is 26 × 10 × 10 × 10 × 10 × 10 × 10 = 26 × 1 000 000.   The correct answer is choice (26 x 1 000 000).
<result>E</result>
The standard model numbers of cell phones in a company are 1 letter followed by 6 digits. How many different model numbers are possible if letters and digits can be repeated?