Question

A license plate consists of two letters followed by three single digits. (a) How many different license plates can be made? (b) How many different license plates can be made if no two-character U.S. state abbreviations are allowed for the two letters?

Answer 1

The license plate is formed by two letters followed by three single digits. There are a total of 26 letters and 10 digits that can be used to form the plate. (a) The first position can be occupied by nay of the 26 letters. Similarly, the second position can also be occupied by nay of the 26 letters. Now, the remaining three positions have to be filled by three single digits. There are total 10 single digits {0,1,23,4,56,789}. So, the third, fourth and fifth positions can be occupied by any of the 10 digits. Therefore, total number of possible combinations (N) for the license plate are: N = 26x26x10x10x10 = 676000 Thus, the total number of possible license plates are 676000 (6) Total number of two character U.S. state abbreviations are 50. It is given that no two- character US state abbreviations are allowed. So, the possible combinations for the first two positions = (26X26)-50 = 626. The remaining three positions can be occupied by any single digit. So, the third, fourth and fifth positions can be occupied by any of the 10 digits. Therefore, total number of possible combinations (N) for the license plate are: N = 626x10x10x10 = 626000 Thus, the total number of possible license plates are 626000.