3.4 EXERCISES 174 CHAPTER 3 Probability For Extra Help: MyLab Statistics Building Basic Skills and Vocabulary 1. When you calculate the number of permutations of n distinct objects taken r at a time, what are you counting? Give an example. 2. When you calculate the number of combinations of r objects taken from a group of n objects, what are you counting? Give an example. True or False? In Exercises 3–6, determine whether the statement is true or false. If it is false, rewrite it as a true statement. 3. A combination is an ordered arrangement of objects. 4. The number of different ordered arrangements of n distinct objects is n!. 5. When you divide the number of permutations of 11 objects taken 3 at a time by 3!, you will get the number of combinations of 11 objects taken 3 at a time. 6. 7C5 = 7C2 In Exercises 7–14, perform the indicated calculation. 7. 9P5 8. 14P3 9. 8C3 10. 21C8 11. 8 C4 12C6 12. 10 C7 14C7 13. 3 P2 13P1 14. 7 P3 12P4 In Exercises 15–18, determine whether the situation involves permutations, combinations, or neither. Explain your reasoning. 15. The number of ways 16 floats can line up in a row for a parade 16. The number of ways a four-member committee can be chosen from 10 people 17. The number of ways 2 captains can be chosen from 28 players on a lacrosse team 18. The number of four-letter passwords that can be created when no letter can be repeated Using and Interpreting Concepts 19. Video Games You have seven different video games. How many different ways can you arrange the games side by side on a shelf? 20. Skating Eight people compete in a short track speed skating race. Assuming that there are no ties, in how many different orders can the skaters finish? 21. Security Code In how many ways can the letters A, B, C, D, E, and F be arranged for a six-letter security code? 22. Starting Lineup The starting lineup for a softball team consists of 10 players. How many different batting orders are possible using the starting lineup?
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