Problem 6. NFL Stadium Tour (12 points) One of my current hobbies is attempting to see all 32 NFL teams play at their home stadium. For the following problems, note the instructions on the cover page regarding simplifying answers. (a) [2 pts.] Currently, I have seen 18 teams play at home. Based on this information alone, how many different possibilities are there for the set of teams that I've seen play at home? (b) [5 pts.] I have seen 3 out of 4 west coast teams play at home, 5 out of 8 central time zone teams play at home, and 1 out of 3 Florida teams play at home. If I asked you to guess the set of 9 teams from the west coast, central time zone, or Florida that I've seen play at home, what is the maximum number of guesses you would need (i.e. how many valid groups of teams are there that meet the above constraints)? Describe how you arrived at your solution. Note that the sets of west coast, central time zone, and Florida teams are all disjoint. (c) [5 pts.] Suppose that I give you the additional information that I have seen exactly one of the Los Angeles Rams (a west coast team) and the Jacksonville Jaguars (a Florida team) play at home. Given the above information in part (b) is still true, what is the new maximum number of guesses one should need to determine the correct set? Describe how you arrived at your solution