Suppose that a company wants to get a better handle on operational losses at its manufacturing plants caused by malfunctioning equipment, so it decides to institute three-person monitoring and analysis teams chosen from management at each of its plants. At each plant, the management teams take a test to measure knowledge of the manufacturing process, and the three highest-scoring managers will be appointed to the monitoring team.
1) At a particular plant, there are six managers. After taking the exam, how many possible ways can the six managers be ranked?
2) What is the probability that three particular managers - John, Sylvia and Nancy - will be the three highest finishers (in any order) and therefore chosen to be on the new team?
3) The team wants to plan for the number of technicians needed to fix equipment failures that lead to operational losses. If each failure is equally likely to require 2, 3, 5 or 7 technicians to repair it, what is the expected number of technicians needed to fix a failure?