1095 11.6 Basics of Counting Theory Use the fundamental principle of counting to solve each problem. See Examples 1–3. 7. On a business trip, Terry took 3 pairs of pants, 4 shirts, 1 jacket, and 2 pairs of shoes. Determine the number of outfits that Terry can choose. 8. When saddling her horse, Callie can choose from 2 saddles, 3 blankets, and 2 cinches. Find the number of possible choices for saddling Callie’s horse. 9. A conference schedule offers 2 main sessions, 20 break-out sessions, and 4 minicourses. In how many ways can an attendee choose 1 of each to attend? 10. A convenience store offers 16 types of soda with 4 options for flavoring and either crushed or cubed ice. Determine the total number of drink options available for selecting 1 soda with 1 flavor and 1 type of ice. 11. A college has 7 portraits of past college presidents to arrange in a row on a wall. How many different arrangements are possible? 12. A telephone messaging system requires a 4-digit security code. How many security codes are possible if numbers may be repeated? 13. In how many ways can judges select a 1st-place winner, a 2nd-place winner, and a 3rd-place winner from 16 desserts entered in a cooking contest? 14. In how many different ways can 4 different boys be selected from a group of 25 boys on a track team to receive 4 different awards? Evaluate each expression. See Examples 4–8. 15. P112, 22 16. P15, 22 17. P19, 22 18. P110, 42 19. P15, 12 20. P16, 12 21. C14, 22 22. C19, 32 23. C16, 02 24. C18, 02 25. C112, 42 26. C116, 32 Use a calculator to evaluate each expression. See Examples 4 and 7. 27. 20P5 28. 100P5 29. 15P8 30. 32P4 31. 20C5 32. 100C5 33. 15C8 34. 32C4 35. Decide whether the situation described involves a permutation or a combination of objects. See Example 9. (a) a telephone number (b) a Social Security number (c) a hand of 5 cards (d) a committee of politicians (e) the “combination” on a padlock (f) an automobile license plate (g) a lottery choice of six numbers where order does not matter 36. Concept Check What is the difference between a permutation and a combination? Give an example of each. Use the fundamental principle of counting or permutations to solve each problem. See Examples 1–6. 37. Home Plan Choices How many different types of homes are available if a builder offers a choice of 5 basic plans, 4 roof styles, and 2 exterior finishes? 38. Auto Varieties An auto manufacturer produces 7 models, each available in 6 different colors, with 4 different upholstery fabrics, and 5 interior colors. How many varieties of the auto are available? 39. Radio-Station Call Letters How many different 4-letter radio-station call letters can be made under the following conditions? (Disregard the fact that some may be unacceptable for various reasons.) (a) The first letter must be K or W, and no letter may be repeated. (b) Repetitions are allowed (but the first letter is K or W). (c) The first letter must be K or W, the last letter must be R, and repetitions are not allowed.
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