166 homework problems, 12B-copyright Joe Kahlig Chapter 2, Page 1Chapter 2 Homework ProblemsCompiled by Joe KahligSection 2.11. An automobile dealer offers five models. Each modelcomes in a choice of four colors, three types of stereoequipment, and with or without air conditioning. In howmany different ways can a customer orde r an auto fromthis dealer?2. A license plate consists of three letters followed by twodigits. How many different license plates are possible ifthe letters must be different and all of the digits are even?3. How many different four digit numbers ar e there that areodd and greater than 6000?4. How many five digit numbers are multiples of five andgreater than 29,999?5. An exam consists of 6 true/false questions and 5 multi-ple choice questions, each with 4 possible answers. Howmany ways can the exam be worked if each question isanswered?6. An exam consists of 15 multiple choice questions. Thefirst nine questions each have 4 choices and the last 6questions each have 6 choices. How many ways can theanswer sheet be turned in if students are allowed to leavequestions blank?7. How many three-letter identification codes can be con-structed from the first 15 letters of the alphabet if thefirst letter must be a B, a C, or a D and no letters mayoccur more than once.8. Five boys and 4 girls are to be seated in a row that has9 seats.(a) How many ways can this be done if they alternateseats?(b) How many ways can this be done if the girls sittogether?9. How many ways can 7 boys and 4 girls be placed in arow and have them alternate seats?10. Susan, Sara, J ill, Fred, Jim, Jacob, and Randy sit in arow with Jac ob or Fred in the middle seat and Ra ndysitting next to Susan. How many ways can this be done?11. A license plate in the metropolis Metropolitan Area con-sists of two letters and then two digits followed by eithera bat logo or an S. The two letters must be differentand neither digit is permitted to be a zero. How manydifferent license plates are possible?12. A license plate in the metropolis Metropolitan Area con-sists of two letters and two digits followed by either a batlogo or an S. The two letters must b e different and nei-ther digit is permitted to be a zero. How many differentlicense plates are possible?13. Serial numbers assigned to a bicycle by a manufacturehave a first symbol of J, H, o r T to indicate the plant inwhich made, followed by 01, 02, 0 3,..., or 12 to indicatethe month in which ma de, followed by four digits. Howmany different serial numb e rs are po ssible?14. In how many ways can you get a license plate consistingof thr ee letters and two digits in any order with no digitor letter repeated?15. You have 11 different books to place on a shelf. Four ofthe books are blue, 5 are green and 2 are red. In howmany ways can all of the books be arranged on a shelf ifbooks of the same color are to be placed together?16. You have 3 different books written by Tom Clancy, 2different books written by Zane Gray, 6 different booksby R.A. Salvatore, and 5 different books written by JimButcher. How many ways can you arrange the b ooks ona shelf if the books are grouped by author?17. A carnival has a game where you roll three dice: one red,one green, and one blue. A player will win money if oneor more fives are rolled. How many ways can somebodywin at this game?18. A yellow and black six-sided die are added to the gamein problem 17. Now how many ways can somebody winat the game?19. Four people are asked to write down an integer b etween1 and 13 inclusive. How many ways can exactly 2 of thepeople pick an even number ?20. How many 4 symbol computer co de s ca n be made usingthe le tters A, B, E, G, H ,I, J and K if the code hasto have at least one vowel? An example of a valid codeis ABBA.21. For a group of four people. How many ways can two ofthe people have the same birthday and everybody elsehave a different birthday?22. A club is comprised o f 6 guys and 9 girls. How many dif-ferent photos can be made that consist of 5 club membersin a row with the guys and girls alternate positions?23. How many 3 digit numbers have at least one seven inthem?Additional problems covering the multiplication prin-ciple with streaming video solutions can be found inCounting Handout #1 located in the extra handoutsection on the class web page.166 homework problems, 12B-copyright Joe Kahlig Chapter 2, Page 2Section 2.224. Compute the following.(a) C(4, 2)C(48, 3)+C(4, 3)C(48, 2)+C(4 , 4)C(48, 1) =(b) C(52, 5) − [C(4, 0)C(48, 5) + C(4, 1)C(48 , 4)] =(c)10!3!4!2!=(d) C(5, 3)P (6, 3) =(e) 13C(4, 3) ∗ 12C(4, 2) =(f)73− 773=(g)C(12, 8)C(13, 2) + C(12, 9)C(13, 1) + C(12, 10)C(25, 10)=(h) C(450, 1) =(i) P (450, 1) =(j) C(450, 0) =(k) P (450, 0) =(l) 4!C(5, 2 )P (5, 3) =25. From a pool of 7 secretaries, three are selected to beassigned to 3 managers, one per mana ger. In how manyways can they b e selected and assigned?26. How many 6 card hands are possible that have exactlytwo hearts and exactly three spades?27. Five freshmen, fo ur sophomore s, and two juniors arepresent a t a meeting of students. In how many wayscan a six-member committee that contains three fresh-men and two sophomores be formed?28. A child has a set of plastic objects. There are 2 pyramids(all identical), 3 cubes (all identical), and 6 spheres (allidentical). How many ways can the child place all of theobjects in a row.29. A company has five vacancies in its executive traineeprogram. In how many ways can the company selectfive trainees from a group of ten female and eight maleapplicants if the vacancies must b e filled by two womenand three men?30. Codes to identify entries in a computer file are formedby using sequences of four zeros and six ones. How manysuch sequences are possible?31. A prize committee is awarding prizes to 7 differe nt peo-ple. In how many ways can 3 different prize s be awardedso that no person can win more than two prizes?32. The Scholarship Committee nee ds to select a recipient foreach of 4 different scholarships from a pool of 15 appli-cants. How many ways can the scholarships be awardedto the applicants, if no applicant can win more than onescholarship?33. How many 6- person committees are po ssible from agroup of 12 people if:(a) Jim, Susan, and Mary must be on the committee?(b) Only one of the gr oup of Jim, Susan, or Mary mustbe on the committee?34. How many different ways can the letters of the workBOOKKEEPER be arr anged?35. How many different ways can I rearrange the letters ofthe