License plate numbers in a certain state consists of seven characters. The first character is a digit (0 through 9). The next four characters are capital letters (A through Z) and the last two characters are digits. Therefore, a license plate number in this state can be any string of the form: Digit-Letter-Letter-Letter-Letter-Digit-Digit (a) How many different license plate numbers are possible?

Answer:67,600Step-by-step explanation:For the first and last two characters, there are ten possible digits (0 through 9) for each character.For the second through sixth character, there are 26 possible letters (A through Z) for each character.The number of all possible license plate combinations "n" is given by the multiplication of each digits range of possible outcomes:[tex]n=10*26*26*26*26*10*10\\n=456,976,000[/tex]Since there are no restrictions for repeated characters, there are 456,976,000 different license plate numbers are possible.