1117 Let Sn represent the given statement, and use mathematical induction to prove that Sn is true for every positive integer n. 51. 1 + 3 + 5 + 7 + g+ 12n - 12 = n2 52. 2 + 6 + 10 + 14 + g+ 14n - 22 = 2n2 53. 2 + 22 + 23 + g+ 2n = 212n - 12 54. 13 + 33 + 53 + g+ 12n - 123 = n212n2 - 12 Evaluate each expression. 55. P19, 22 56. P16, 02 57. C18, 32 58. 9! 59. C110, 52 60. 10 # 9! Solve each problem. 61. Median Annual Earnings In 2017 the median annual earnings of a high school graduate with no college attendance was $37,024. This amount is expected to increase by about $884 per year. How much will a person earning the median amount earn until retirement if he or she joins the work force at age 18 and works until age 66? (Data from U.S. Bureau of Labor Statistics.) 62. Median Annual Earnings In 2017 the median annual earnings of a person with 4 yr of college was $60,996. This amount is expected to increase by about $936 per year. How much will a person earning the median amount earn until retirement if he or she joins the work force at age 22 and works until age 66? (Data from U.S. Bureau of Labor Statistics.) 63. Median Annual Earnings Refer to Exercises 61 and 62. How much more will a person with 4 yr of college who earns the median amount make during his or her career than a person with no college attendance who earns the median amount during his or her career? If the expenses of a 4-yr college degree are estimated at $101,160, is earning a 4-yr college degree worth it? (Data from U.S. Bureau of Labor Statistics.) 64. Wedding Plans Two people are planning their wedding. They can select from 2 different chapels, 4 soloists, 3 organists, and 2 ministers. How many different wedding arrangements are possible? 65. Couch Styles Bob is furnishing his apartment and wants to buy a new couch. He can select from 5 different styles, each available in 3 different fabrics, with 6 color choices. How many different couches are available? 66. Summer Job Assignments Four students are to be assigned to 4 different summer jobs. Each student is qualified for all 4 jobs. In how many ways can the jobs be assigned? 67. Conference Delegations A student council consists of 6 seniors and 3 juniors. Three members are to be selected to attend a conference. (a) How many different such delegations are possible? (b) How many are possible if 2 seniors and 1 junior must attend? 68. Tournament Outcomes Nine football teams are competing for first-, second-, and third-place titles in a statewide tournament. In how many ways can the winners be determined? CHAPTER 11 Review Exercises
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