Answer to Question #15026 in Combinatorics | Number Theory for abdel007
There are 20 people on the board of directors of a publicly listed company. Each pair of people are either friends or enemies with each other. Every person has exactly 6 enemies on the board. If every group of 3 directors form a committee, what is the total number of committees that are formed by all friends or all enemies?
At first, let's see the possibilities of one person. A person has 6 enemies and 14 friends. He can form a committee of other two members by either selecting 2 from 6 enemies or 2 from 14 friends. That can be done in