1096 CHAPTER 11 Further Topics in Algebra 40. Meal Choices A menu offers a choice of 3 salads, 8 main dishes, and 5 desserts. How many different 3-course meals (salad, main dish, dessert) are possible? 41. Arranging Blocks Baby Finley is arranging 7 blocks in a row. How many different arrangements can he make? 42. Names for a Baby A couple has narrowed down the choice of a name for their new baby to 5 first names and 3 middle names. How many different first- and middle-name combinations are possible? 43. License Plates For many years, the state of California used 3 letters followed by 3 digits on its automobile license plates. (a) How many different license plates are possible with this arrangement? (b) When the state ran out of new plates, the order was reversed to 3 digits followed by 3 letters. How many additional plates were then possible? (c) When the plates described in part (b) were also used up, the state then issued plates with 1 letter followed by 3 digits and then 3 letters. How many plates does this scheme provide? 44. Telephone Numbers How many 7-digit telephone numbers are possible if the first digit cannot be 0 and the following conditions apply? (a) Only odd digits may be used. (b) The telephone number must be a multiple of 10 (that is, it must end in 0). (c) The telephone number must be a multiple of 100. (d) The first 3 digits are 481. (e) No repetitions are allowed. 45. Seating People in a Row In an experiment on social interaction, 9 people will sit in 9 seats in a row. In how many ways can this be done? 46. Genetics Experiment In how many ways can 7 of 10 tomato plants be arranged in a row for a genetics experiment? 47. Course Schedule Arrangement A business school offers courses in keyboarding, spreadsheets, transcription, business English, technical writing, and accounting. In how many ways can a student arrange a schedule if 3 courses are taken? 48. Course Schedule Arrangement If your college offers 400 courses, 20 of which are in mathematics, and your counselor arranges your schedule of 4 courses by random selection, how many schedules are possible that do not include a math course? 49. Club Officer Choices In a club with 15 members, in how many ways can a slate of 3 officers consisting of president, vice-president, and secretary/treasurer be chosen? 50. Batting Orders A baseball team has 20 players. How many 9-player batting orders are possible? 51. Letter Arrangement Consider the word BRUCE. (a) In how many ways can all the letters of the word BRUCE be arranged? (b) In how many ways can all the first 3 letters of the word BRUCE be arranged? 52. Basketball Positions In how many ways can 5 players be assigned to the 5 positions on a basketball team, assuming that any player can play any position? In how many ways can 10 players be assigned to the 5 positions? Finley
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