1. Composite sampling is a way to reduce laboratory testing costs. A public health department is testing for possible fecal contamination in public swimming pools. In this case, water samples from 5 public swimming pools are combined for one single test, and further testing is performed only if the combined sample shows fecal contamination. Based on past experience, there is a 3% chance of finding fecal contamination in a public swimming area. What is the probability that a combined sample from 5 public swimming pools has fecal contamination?
2. Peter, Paul, Mary, Andrew, John, and Martha are members of the pastoral council at a local church. They are to be seated at one side of a long conference table in a pastoral council meeting.
a. How many possible ways can these 6 council members can be seated?
b. How many possible sitting arrangements are there if only gender is considered in the process?
3. A banquet organizer knows that not all 600 invited guests will show up at an event. Based on past experience, only 80% of the invited guest for this special event will come. When expensive dishes are served, it would be prudent not to order the full 600 plates because a good number of them will be wasted. On the other hand, the banquet organizer will try to stay within 7% probability that he would not have to rush to prepare the expensive dishes. How many of these expensive dishes would you order if you were organizing this banquet?