736 CHAPTER 11 Probability Exercises Warm Up Exercises In Exercises 1– 6, fill in the blank with an appropriate word, phrase, or symbol(s). 1. A distinct group of objects without regard to their arrangement is called a(n) ________. Combination 2. The symbol for the number of combinations when r items are selected from n distinct items is ________. Cn r 3. If we want to select r items from n items, and the order of the arrangement is important, then ________ are used. Permutations 4. If we want to select r items from n items, and the order of the arrangement is not important, then ________ are used. Combinations Practice the Skills In Exercises 5– 6, determine whether the description given describes a permutation or a combination. 5. Softball Team Jocelyn is the manager of the Central Carolina Community College softball team. The team has 16 players. a) Jocelyn selects 9 players for the batting order of today’s game. Permutation b) Jocelyn selects 5 players to volunteer at the school’s open house. Combination 6. Smartphone Photos Sundar has 20,291 photos on his smartphone. a) Sundar selects and deletes 500 photos to have enough storage to download a new app. Combination b) Sundar selects 25 photos to place in order for a Power Point presentation. Permutation In Exercises 7–20, evaluate the expression. 7. C5 3 10 8. C8 2 28 9. a) C6 4 15 b) P6 4 360 10. a) C7 2 21 b) P7 2 42 11. a) C8 0 1 b) P8 0 1 12. a) C 12 8 495 b) P 12 8 19,958,400 13. a) C 10 3 120 b) P 10 3 720 14. a) C5 5 1 b) P5 5 120 15. C C 3 2 13 2 1 26 16. C C 5 3 9 3 5 42 17. C C 8 5 14 5 4 143 18. C C 4 2 8 2 3 14 19. C C 4 3 10 3 1 30 20. C C 6 4 10 4 1 14 Problem Solving 21. Hiring There are 10 qualified applicants for 3 security positions at a hospital. In how many ways can the positions be filled? 120 22. Banana Split An ice-cream parlor has 20 different flavors. Cynthia orders a banana split and has to select 3 different flavors. How many different selections are possible? 1140 23. Test Essays Tina must select and answer in any order four of six essay questions on a test. In how many ways can she do so? 15 24. Software Packages During a special promotion at Dell, a customer purchasing a computer is given the choice of 2 free software packages. If there are 9 different software packages from which to select, how many different ways can the 2 packages be selected? 36 25. Scholarships A scholarship committee has received 8 applications for a $500 scholarship. The committee has decided to select 3 of the 8 candidates for further consideration. In how many ways can the committee do so? 56 26. Quinella Bet A quinella bet consists of selecting the first- and second-place winners, in any order, in a particular event. For example, suppose you select a 2–5 quinella. If 2 wins and 5 finishes second, or if 5 wins and 2 finishes second, you win. Sven goes to a jai alai match. In the match, 8 jai alai teams compete. How many quinella tickets must Sven purchase to guarantee a win? 28 m Jai Alai 27. Pennsylvania Lottery Match 6 Lotto is a Pennsylvania lottery game in which players select 6 different numbers, AA World Travel Library/Alamy Stock Photo SECTION 11.8 Stockcreations/Shutterstock
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