Use the fundamental counting principle to solve the problem.
-How many license plates can be made consisting of 3 letters followed by 2 digits?
A)1,757,600
B)100,000
C)11,881,376
D)175,760

Question

Quizplus · Accepted Answer

There are 26 choices for each of the 3 letters (26x26x26) and 10 choices for each of the 2 digits (10x10). Using the fundamental counting principle, we multiply the number of choices for each set of characters: (26x26x26)(10x10) = 1,757,600. Therefore, the answer is A) 1,757,600. There are 26 letters in the alphabet, so there are 26 choices for the first letter, 26 choices for the second letter, and 26 choices for the third letter. There are 10 digits (0-9), so there are 10 choices for the fourth digit and 10 choices for the fifth digit. Therefore, by the fundamental counting principle, the total number of license plates that can be made is 26 x 26 x 26 x 10 x 10 = 1,757,600.

Use the Fundamental Counting Principle to Solve the Problem