SECTION 3.4 Additional Topics in Probability and Counting 175 23. Footrace There are 72 runners in a 10-kilometer race. How many ways can the runners finish first, second, and third? 24. Singing Competition There are 16 finalists in a singing competition. The top five singers receive prizes. How many ways can the singers finish first through fifth? 25. Playlist A band is preparing a setlist of 21 songs for a concert. How many different ways can the band play the first six songs? 26. Archaeology Club An archaeology club has 38 members. How many different ways can the club select a president, vice president, treasurer, and secretary? 27. Blood Donors At a blood drive, eight donors with type O+ blood, six donors with type A+ blood, and three donors with type B+ blood arrive. In how many distinguishable ways can the donors stand in line? 28. Necklaces You are putting nine blue glass beads, three red glass beads, and seven green glass beads on a necklace. In how many distinguishable ways can the colored beads be put on the necklace? 29. Letters In how many distinguishable ways can the letters in the word statistics be written? 30. Computer Science A byte is a sequence of eight bits. A bit can be a 0 or a 1. In how many distinguishable ways can you have a byte with five 0’s and three 1’s? 31. Experiment A researcher is randomly selecting a treatment group of 10 human subjects from a group of 20 people taking part in an experiment. In how many different ways can the treatment group be selected? 32. Jury Selection From a group of 36 people, a jury of 12 people is selected. In how many different ways can a jury of 12 people be selected? 33. Students A class has 40 students. In how many different ways can three of the students be selected to work on a class project together? (Assume the order of the students is not important.) 34. Lottery Number Selection A lottery has 52 numbers. In how many different ways can six of the numbers be selected? (Assume the order of selection is not important.) 35. Menu A restaurant offers a dinner special that lets you choose from 10 entrées, 8 side dishes, and 13 desserts. The dinner special includes one entrée, two side dishes, and one dessert. Assume the side dishes are not the same. How many different meals are possible? 36. Floral Arrangements To create a floral arrangement with six different colored roses, three different colored carnations, and three different colored daisies, you choose from eight different colors of roses, six different colors of carnations, and seven different colors of daisies. How many different arrangements are possible? 37. Water Pollution An environmental agency is analyzing water samples from 80 lakes for pollution. Five of the lakes have dangerously high levels of dioxin. Six lakes are randomly selected from the sample. Use technology to find how many ways one polluted lake and five nonpolluted lakes can be chosen. 38. Property Inspection A property inspector is visiting 24 properties. Six of the properties are one acre or less in size, and the rest are greater than one acre in size. Eight properties are randomly selected. Use technology to find how many ways three properties that are each one acre or less and five properties that are each larger than one acre can be chosen.
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