Combinatorics : The HARD Round Table !

As promised, we do the "hard" version of the round table problem. For a great alternative approach see Counting: An Introduction to Enumerative Combinatorics https://amzn.to/3Zts7dE . 1) 14 knights sit around a round table (fixed positions), and 3 are picked for a quest. If NO 2 picked knights can have sat next to each other (with respect to the original seating), how many questing groups can be chosen? 2) k knights sit around a round table (fixed positions), and p are picked for a quest. If NO 2 picked knights can have sat next to each other (with respect to the original seating), how many questing groups can be chosen? 3) k knights sit around a round table (fixed positions), and p are picked for a quest. If there are at least s knights between any two of the picked knights (with respect to the original seating), how many questing groups can be chosen? #combinatorics #roundtable #combinations