Discrete math ( only answer if you can answer all, you! )1) there are eight different jobs in a printer queue. each job has a distinct tag which is a string of three upper case letters. the tags for the eight jobs are: {lpw, qkj, cdp, usu, bbd, pst, lsa, rhr}(a) how many different ways are there to order the eight jobs in the queue? (b) how many different ways are there to order the eight jobs in the queue so that job usu comes immediately before cdp? (c) how many different ways are there to order the eight jobs in the queue so that job usu comes somewhere before cdp in the queue, although not necessarily immediately before? (d) how many different ways are there to order the eight jobs in the queue so that either qkj or lpw come last? (e) how many different ways are there to order the eight jobs in the queue so that qkj is either last or second-to-last? 2) (6 points) license plate numbers in a certain state consists of seven characters. the first character is a non-zero digit (1 through 9). the next four characters are capital letters (a through z) and the last two characters are non-zero digits. therefore, a license plate number in this state can be any string of the form: digit-letter-letter-letter-letter-d igit-digit(a) how many different license plate numbers are possible? (b) how many license plate numbers are possible if no digit appears more than once? (c) how many license plate numbers are possible if no digit or letter appears more than once?