11.8 Combinations 737 in any order, from 1 to 49, inclusively. How many different sets of 6 numbers can be chosen? 13,983,816 28. Texas Lottery Lotto Texas is a Texas lottery game in which players select 6 different numbers, in any order, from 1 to 54, inclusively. How many different sets of 6 numbers can be chosen? 25,827,165 29. Shirts Matthew has 12 shirts in his closet and must select 4 to take with him on vacation. In how many ways can Matthew select the shirts? 495 30. Shoe Donation Dirk owns 45 pairs of shoes and would like to donate 10 pairs to Goodwill. How many different ways can Dirk select the pairs of shoes? 3,190,187,286 31. Full House If 5 cards are dealt from a standard 52-card deck, how many different ways can 3 kings and 2 queens be dealt? 24 32. Four of a Kind If 5 cards are dealt from a standard 52card deck, how many different ways can 4 aces and 1 other card that is not an ace be dealt? 48 33. Choosing Volunteers Kipsie is the athletic director at Owens Community College. She must select 5 tennis players and 5 basketball players to volunteer at the school’s community showcase. She can choose from 9 tennis players and 15 basketball players. How many different ways can she select the volunteers? 378,378 34. Test Question On an English test, Tito must write an essay for three of the five questions in Part 1 and four of the six questions in Part 2 in any order. How many different combinations of questions can he answer? 150 35. Cheese and Fruit Gift Basket Sinead is buying a gift basket that consists of 5 types of cheese and 3 types of fruit. She can choose from 11 different types of cheese and 7 different types of fruit. Based on these two choices, how many different gift baskets are available? 16,170 36. Newsletter An animal shelter has 15 cats and 12 dogs available for adoption. The shelter wants to select 6 cats and 4 dogs to feature in the adoption newsletter. In how many ways can this be done? 2,477,475 37. Real Estate Flier Bobby is selling his house and is preparing a flier to give to potential buyers. On the flier, Bobby wishes to put 2 photos of the outside of the house and 4 photos of the inside of the house. He has 7 photos of the outside and 11 photos of the inside to choose from. How many different ways can the flier be prepared? 6930 38. Forming a Committee The Philadelphia City Council is forming a committee to explore ways to improve public transportation in the city. The committee will consist of 4 representatives from the city council and 3 representatives from a citizens advisory board. If there are 7 city council members and 5 citizens advisory board members from which to choose, how many different ways can the committee be formed? 350 39. Hummus and Chips Derrin is bringing three types of hummus and two types of chips to a potluck luncheon. His choices for hummus are classic, red pepper, garlic, spinach, jalapeño, edamame, siracha, and avocado. His choices for chips are pita, bagel, blue corn, yellow corn, white corn, cheddar, multigrain, sweet potato, and lime. Based on these two choices, how many different selections of hummus and chips does Derrin have? 2016 40. Chili Recipe Christoph is making chili. He wishes to include 3 types of beans, and his choices are kidney, pinto, red, black, garbanzo, fava, and navy. He wishes to include 4 types of peppers, and his choices are red bell, green bell, orange bell, yellow bell, jalapeno, habanero, poblano, and datil. Based on these two choices, how many different varieties of chili can Christoph make? 2450 41. Selecting Mutual Funds Hamid recently graduated from college and now has a job that provides a retirement investment plan. Hamid wants to diversify his investments, so he wants to invest in four stock mutual funds and two bond mutual funds. If he has a choice of eight stock mutual funds and five bond mutual funds, how many different selections of mutual funds does he have? 700 42. Baseball Lineup Warez is the manager of the Bradenton Wildcats baseball team. He already has selected his pitcher and catcher, but he needs to choose 3 outfielders and 4 infielders. He has 7 outfielders and 8 infielders available to choose from. Based on these two choices, how many different selections does Warez have? 2450 43. New Products Nabisco is testing 5 chocolate chip cookies, 4 crackers, and 6 low-carb snacks. If it plans to market 2 of the chocolate chip cookies, 3 of the crackers, and 2 of the low-carb snacks, how many different combinations are possible? 600 44. Catering Service A catering service is making up trays of hors d’oeuvres. The hors d’oeuvres are categorized as inexpensive, average, and expensive. If the client must select three of the eight inexpensive, five of the nine average, and two of the four expensive hors d’oeuvres, how many different choices are possible? 42,336 Challenge Problems/Group Activities 45. Test Answers Consider a 10-question test in which each question can be answered either correctly or incorrectly. a) How many different ways are there to answer the questions so that eight are correct and two are incorrect? 45 b) How many different ways are there to answer the questions so that at least eight are correct? 56 Brent Hofacker/Shutterstock
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