Stat 300 - Woodmansee Group Work 3.4 Name: For each question, show work using notation from section 3.4. Use the I key on your calculator. 1. Eight people complete in a downhill race. Assuming that there are no ties, in how many different orders can the skiers finish? 2. There are 16 finalists in a signing competition. The top five singers receive prizes. How many ways can the singers finish first through fifth? 3. You are putting 9 pieces of blue beach glass, 3 pieces of red beach glass, and 7 pieces of green beach glass on a necklace. In how many distinguishable ways can the beach glass be put on the necklace? 4. From a group of 40 people, a jury of 12 is selected. In how many different ways can a jury of 12 people be selected? 5. An environmental agency is analyzing soil samples from 50 farms for lead contamination. Eight of the farms have dangerously high levels of lead. Ten farms are randomly selected from the sample. How many ways could two contaminated farms and eight noncontaminated farms be chosen? Hint: Look at how the author gets 31,049,370 in the first part of the solution to Example 8 on page 173. 6. The U.S. Senate Subcommittee on Fiscal Responsibility and Economic Growth has five members. Each member is equally likely to serve in any of the positions. What is the probability of making a randomly selecting the chairman and the ranking member, in that order? A pizza show offers nine toppings. Assume that toppings have an equal chance of being selected that that no topping is used more than once. What is the probability that the toppings on a three- topping pizza are pepperoni, onions, and mushrooms