Solve the problem.
-If a license plate consists of two letters followed by four digits, how many different licenses could be created having at least one letter or digit repeated.
A)3,484,000 licenses
B)6,760,000 licenses
C)4,009,824 licenses
D)3,276,000 licenses

Question

Quizplus · Accepted Answer

There are 26 possible letters and 10 possible digits. For the first letter, there are 26 choices. For the second letter, there are 25 choices (since it cannot be the same as the first letter). For the first digit, there are 10 choices. For the second digit, there are 10 choices. For the third digit, there are 10 choices. For the fourth digit, there are 10 choices. So, the total number of possible license plates is 26 * 25 * 10 * 10 * 10 * 10 = 6,760,000. However, we need to subtract the number of license plates that do not have at least one letter or digit repeated. There are 26 * 25 * 10 * 10 * 10 * 10 = 6,760,000 such license plates. So, the total number of possible license plates that have at least one letter or digit repeated is 6,760,000 - 3,276,000 = 3,484,000.

Solve the Problem. -If a License Plate Consists of Two Letters Followed by Letters