1. A tweet (a message posted on Twitter) is a sequence of at most 140 characters. Assuming there are 256 valid different characters that can appear in each position, how many distinct tweets are possible? 2. Cars in the United States display license plates containing an alphanumeric code, whose format varies from state to state. Each of the following questions describes the format of currently issued license plates by some state. For each, determine the number of different license plate codes (often misleadingly called license plate numbers despite the presence of letters) of the listed form. All letters in all codes are upper case. a. Minnesota: digit-digit-digit-letter-letter-letter (example: 400GPA). b. Pennsylvania: letter-letter-letter-digit-digit-digit-digit (example: EEE2718). c. Connecticut: digit-letter-letter-letter-letter-digit (example: 4FIVE6). 3. A particular voicemail system allows numerical passwords of length 3, 4, or 5 digits. How many passwords are possible in this system?