1 Instructions: Kindly provide the correct solutions to the problems below as a Single PDF le. All work submitted must be your own original work. No outside help of any kind is allowed on this exam except for the use of the class notes, class Videos, and any other content that is posted to our blackboard page. 1. To purchase a lunch special at Darryl's Diner, you must select a sandwich, a side, and a soda. For sandwich, you can choose turkey, ham, or salami. As a side, you may select from soup, salad, or chips. For soda, you may select Coke Zero, Sprite, seltzer, or Mountain Dew. In total, how many different lunch specials can be Grated? 2. Playing cards come in four suits: hearts, clubs, diamonds, and spades. What is the minimum number of playing cards you need in your hand to guarantee that 7 of them are of the same suit? 3. Answer the following: (a) What is the coefcient of $83411 in (a: + y)19 (b) What is the coefficient of xsyll in (3x + 73;)\" (c) What is the coefcient of x8 in (x 1)19 4. The Mathematics Department at Hogwarts school of Witchcraft and Wizardry has 10 junior faculty members and 18 senior faculty members, How many ways are there to form a committee with nine members, if the committee is to have more senior faculty than junior faculty? 5. Let D = {1,2,3,4,5,6} and E = {a,e,z',0,u} (a) How many functions are there from D to E? (b) How many one-toone functions are there from D to E? Explain your reasoning (c) How many functions are there from D to E that send 3 to e? . At Euler's Federal Savings Bank, all ATM access codes can be any strings of either six or seven decimal digits. (a) How many different ATM access codes are available at Euler's Federal Savings Bank? (b) How many ATM access codes contain only even digits? (0) How many ATM access codes contain at least one odd digit? . Each of the following statements are true. Using methods discussed in class, justify each off them. (a) 12712 1512n + 4 is (9(4n3) (b) ($311) is (9%) (c) The function f (x) = [x] is C(30)