8. For each of the following setups, specify the correct counting formula between (i)(v) to use, specify the values of n and 7", and explain why it is correct. If you answer \"None of these,\" please provide the formula that would be correct. (10 points) (i) LI (ii) nit (m) ('7'), (iv) (\"H i 1), (v) None of these (n 7 7'). r r a) An assembly operation in a manufacturing plant requires three steps that can be performed in any sequence. How many different ways can the assembly be performed? (2 points) b) An upscale restaurant offers a special prix fixe menu in which, for a fixed dinner cost, a customer selects from four appetizers, three salads, four entrees, and five desserts. How many different dinners are available if a dinner consists of one appetizer, one salad, one entree, and one dessert? (2 points) c) A group of three undergraduate and five graduate students are able to serve on a committee with the student government. How many ways can four students be randomly selected from the group to fill this committee? (2 points) d) When you get a new debit card, you are asked to choose a four-digit personal identification numbers (PIN). How many different Ple can one choose for their debit card? (2 points) e) In the game of dominoes, each piece (i.e., domino) is marked with two numbers. The pieces are symmetrical, so the domino (2, 6) is equivalent to (6, 2). How many different pieces can be formed using the numbers 1,2,--- ,6? (2 points)