Exam II Review ProblemsNote: Not every topic is covered in this review.Please also take a look at the previous Week-in-Reviews for more practice problems.1. You have completely forgotten the combination of your lock. It is one of those “standard” combin ation locks,which uses a three number combin ation with each number in the range of 0 through 39. All you rememberis that the second number is either 27 or 37, while the third number ends in a 5. In desperation, you decideto go through all possible combinations. Assuming that it takes about 10 seconds to try each combination,what is th e longest possible time it can take to open your locker?2. Many U.S. license plates display a sequence of three letters followed by three digits.(a) How many such license plates are possible?(b) In order to avoid confusion of letters with digits, some states do not use the letters I, O or Q on theirlicense plates. How many of these license plates are possible?3. Bill and Sue an d four of their friends go to the movies. They all sit next to each other in the same row .How many ways can this be d on e if(a) Sue and Bill must sit next to each other?(b) Sue must not sit next to Bill?(c) Sue sits on on e end of th e row and Bill sits on the other end of the row?4. Susie has 30 different songs (15 rock, 5 rap, 6 country, and 4 classical) she wants to arrange on her MP3player.(a) How many different playlists of all her songs are possible?(b) How many different playlists are possible if all songs of the same genre must be grouped together?5. A jewelry store chain with 8 stores in Georgia, 12 in Florida, and 10 in Alabama is planning to close 10 ofthese stores.(a) In how many different ways can this be done?(b) The company decided to close 2 stores in Georgia, 5 in Florida, and 3 in Alabama. In how manydifferent ways can this be done?6. How many 4-person committees are possible from a group of 9 people if(a) There are no restrictions?(b) Both Jim and Mary must be on the committee?(c) Either Jim or Mary (but not both) must be on the committee?7. You h ave a box that contains 3 red, 4 black, 2 green, and 5 purple balls. If you take a sample of three ballsfrom the box, in how many ways can you get(a) Exactly 2 black balls and one green ball?(b) No purple balls?(c) At least two pur ple balls?(d) Exactly 2 red balls or exactly one pu rple ball?8. How many different 20-digit numbers can be formed from two 5’s, three 2’s, five 1’s, s ix 4’s, two 3’s, an 8and a 9?9. An author is writing a new book. She has a list of 20 different female n ames and 15 different male names,from which she will choose her 10 character names. In how many different ways can she(a) Choose her 10 characters?(b) Choose half female and half m ale characters?(c) Choose exactly 6 female characters and determine the ord er of appearance of all the characters in herbook?10. From a group of 15 chefs, one executive chef, on e pastry chef and 4 s ou s chefs must be chosen. Assumingall 15 chefs are qualified for all the positions, in how many different ways can the 6 chefs be chosen?11. An experiment consists of tossing a fair 4-sided die and flipping a fair coin.(a) Describe an appropriate sample space for this experiment.(b) Write the event, E, that heads is tossed on the coin.(c) Write the event, F , that tails is tossed on the coin or a 3 is rolled on the die.(d) Are E and F mutually exclusive events? Why or why not?12. A pair of fair 6-sided dice are rolled and the outcomes on each die are recorded.(a) Describe an appropriate sample space for this experiment.(b) How many total events are associated with this experiment?(c) Write the event, E, that a sum of 7 is rolled.13. The following system of inequalities are constraints in a linear programming problem. Graph the feasibleregion. Label all lines and corner points.x − y ≥ 0x + y ≤ 1010x + 9y ≥ 45x ≥ 0y ≥ 0(a) At what point is the objective function f = 5x + 4.5y maximized on this region and what is themaximum value? (If not possible, explain why not.)(b) At what point is the objective function f = 5x+4.5y minimized on this region and what is the minimumvalue? (If not possible, explain why not.)14. SET UP the following Linear Programming problem. DO NOT SOLVE.You man age an ice cream factory that makes three flavors: Vanilla, Chocolate, and Strawberry. Into eachbatch of Vanilla go two eggs, one cup of milk and two cups of cream. Into each batch of Chocolate go oneegg, one cup of milk and two cups of cream, while into each batch of Strawb er ry go one egg, two cups ofmilk and two cups of cream. You have in stock 220 eggs, 120 cups of milk, and 200 cups of cream. You makea profit of $3 on each batch of Vanilla, $2 on each batch of Chocolate, and $4 on each batch of Strawberry.How many batches of each fl avor should you make in order to maximize your profit?15. A company is selling two perfumes, A and B, for $20 and $17 per ounce, respectively. It takes the company3 hou rs and $12 to produce each ounce of perfu me A and 1 hour an d $15 f or each ounce of perfum e B. Ifthe company has a total of 90 hours and $600 for production, and the company is not allowed to make morethan 20 ounces of perfume A, how m any ounces of each perfume should the company produce in order tomaximize its revenue? What is its maximum revenue? Is anything leftover at the optimal production level?16. True or False? U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and A = {0, 1, 2, 3, 4, 5}.T F ∅ ∈ AT F n(A) = 5 T F n({3, 4}) = 2T F ∅ ⊆ AT F {1, 3, 5} ∈ A T F n(∅) = 1T F {1, 2, 3} ⊂ AT F 2 ∈ A T F 10 ∈ ACT F 2 ⊆ AT F {∅} = ∅ T F 0 = ∅17. Given two subsets A and B of U where n(U ) = 85, n(A∪B) = 50, n(A) = 30, and n(B) = 45, find n(A∪BC).18. A = {k, l, b}(a) How many total subsets does th e set A have?(b) List all the subsets of A.(c) How m any of these subsets are proper subsets of A?(d) Give an examp le of two su bsets of A that are disjoint. If this is not possible, then explain why not.19. Shade the part of a Venn diagram that is represented by (AC∪ B) ∩ (C ∪ A)20. Write the set notation that would represent the shaded portion of the Venn diagram.BCA21. U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = …
View Full Document
Unlocking...