12. Stocking a Store A clothing store sells pure wool and polyester-wool suits. Each suit comes in 3 colors and 10 sizes. How many suits are required for a complete assortment? 13. Baseball On a given day, the American Baseball League schedules 7 games. How many different outcomes are possible, assuming that each game is played to completion? 14. Choosing Seats If 4 people enter a bus that has 9 vacant seats, in how many ways can they be seated? 15. Choosing a Team In how many ways can a squad of 4 relay runners be chosen from a track team of 8 runners? 16. Baseball In how many ways can 2 teams from 14 teams in the American League be chosen without regard to which team is at home? 17. Telephone Numbers Using the digits 0, 1, 2, . . . , 9, how many 7-digit numbers can be formed if the first digit cannot be 0 or 9 and if the last digit is greater than or equal to 2 and less than or equal to 3? Repeated digits are allowed. 18. License Plate Possibilities A license plate has 1 letter, excluding O and I, followed by a 4-digit number that cannot have a 0 in the lead position. How many different plates are possible? 19. Binary Codes Using the digits 0 and 1, how many different numbers consisting of 8 digits can be formed? 20. Arranging Flags How many different vertical arrangements are there of 10 flags if 4 are white, 3 are blue, 2 are green, and 1 is red? 21. Forming Committees A group of 9 people is going to be formed into committees of 4, 3, and 2 people. How many committees can be formed if: (a) A person can serve on any number of committees? (b) No person can serve on more than one committee? 22. Birthday Problem For this problem, assume that a year has 365 days. (a) In how many ways can 18 people have different birthdays? (b) What is the probability that no 2 people in a group of 18 people have the same birthday? (c) What is the probability that at least 2 people in a group of 18 people have the same birthday? 23. Unemployment According to the U.S. Bureau of Labor Statistics, 3.8% of the U.S. labor force was unemployed in March, 2024. (a) What is the probability that a randomly selected member of the U.S. labor force was unemployed in March, 2024? (b) What is the probability that a randomly selected member of the U.S. labor force was not unemployed in March, 2024? 24. You have four $1 bills, three $5 bills, and two $10 bills in your wallet. If you pick a bill at random, what is the probability that it will be a $1 bill? 25. Each of the numbers … 1, 2, , 100 is written on an index card, and the cards are shuffled. If a card is selected at random, what is the probability that the number on the card is divisible by 5? What is the probability that the card selected either is a 1 or names a prime number? 26. At the Milex tune-up and brake repair shop, the manager has found that a car will require a tune-up with a probability of 0.6, a brake job with a probability of 0.1, and both with a probability of 0.02. (a) What is the probability that a car requires either a tuneup or a brake job? (b) What is the probability that a car requires a tune-up but not a brake job? (c) What is the probability that a car requires neither a tuneup nor a brake job? The Chapter Test Prep Videos include step-by-step solutions to all chapter test exercises. These videos are available in MyLab™ Math. In Problems 1–4, a survey of 70 college freshmen asked whether students planned to take biology, chemistry, or physics during their first year. Use the diagram to answer each question. 15 22 9 2 7 8 4 U Biology Chemistry Physics 1. How many of the surveyed students plan to take physics during their first year? 2. How many of the surveyed students do not plan to take biology, chemistry, or physics during their first year? 3. How many of the surveyed students plan to take only biology and chemistry during their first year? 4. How many of the surveyed students plan to take physics or chemistry during their first year? In Problems 5–7, compute the value of the given expression. 5. 7! 6. ( ) P 10, 6 7. ( ) C 11, 5 8. M&M’s® offers customers the opportunity to create their own color mix of candy. There are 21 colors to choose from, and customers are allowed to select up to 6 different colors. How many different color mixes are possible, assuming that no color is selected more than once and 6 different colors are chosen? 9. How many distinct 8-letter words (meaningful or not) can be formed from the letters in the word REDEEMED? 10. In horse racing, an exacta bet requires the bettor to pick the first two horses in the exact order. If there are 8 horses in a race, in how many ways could you make an exacta bet? 11. In the state of Ohio, license plates have three letters A–Z ( ) followed by 4 digits 0–9 . ( ) Assume that all letters and digits may be used, except that the third letter cannot be O, I, or Z. If repetitions are allowed, how many different plates are possible? Chapter Test Chapter Test 937
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