When Mr. Bilbo Baggins of Bag End announced that he would shortly be celebrating his eleventy-first birthday with a party of special magnificence, there was much talk and excitement in Hobbiton.

i. Suppose Bilbo plans 11 circular tables with 11 guests at each table. Each table and chair is distinct and numbered. A seating plan assigns each of the 121 guests to a particular table and chair. How many seating plans are possible?

ii. If two guests decline Bilbo's party invitation, now how many seating plans are possible if we consider the empty chairs?

iii. Each table has a flower arrangement with 11 flowers. Bilbo makes the flower arrangement by using any combination of roses, daisies, irises, lillies, and elanor (a golden star-shaped flower that grows in Lothlorien). How many different flower arrangements are possible?

iv. What if Frodo Baggins and Lobelia Sackville-Baggins are two of the eleven guests at one of the tables and they must NOT be seated next to each other. How many distinct and valid seating arrangements are there for this table? Rotating guests around the table does not count as a distinct seating arrangment.