The Federal Bureau of Investigation (FBI) maintains a records system that houses civil background checks and criminal histories in a database. Each file has its own identification number (ID). With its initial algorithm for generating IDs, the system will generate only 400 million unique IDs. Because of the number of individuals in the database, this algorithm was not sufficient—more numbers were needed. The new algorithm consists of eight characters. Each character can be a digit from 0 to 9 or one of 17 letters of the alphabet (letters that can be confused with numbers, such as the number 1 and letter I, are excluded).
(a) To the nearest billion, how many identification numbers are possible with this scheme?
(b) The FBI does not allow the first character to be 0. To the nearest billion, how many identification numbers are possible?
(c) The FBI does not allow any combinations of letters that spell out obscenities. So, there are 271 billion unique ID numbers that can be created by the new FBI algorithm. Based on your answer to part (b), how many combinations of obscenities are possible with the new FBI algorithm?