Question: A hostess wishes to invite 6 dinner guests from a list of 14 friends
1. How many sets of guests are possible?
2. How many sets of guests are possible if 6 friends are boring and 6 friends are interesting, and the hostess wants to have at least 1 of each?
3. How many sets of guests are possible if 2 of the friends dislike each other and neither will come if he other is present?
4. How many sets of guests are possible if 2 of the friends are very fond of each other and one won't come without the other?