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?

Question

agent47 · Answer

Suppose you pick one guy, say director 1:
So it's 20C1 = 20.
Now you have to pick 2 people who are not his enemies: 20-6=14 friends, so 14C3

agent47 · Answer

So a way to pick a committee consisting of all friends would be 20C1*14C3

agent47 · Answer

I mean 20C1*14C2

agent47 · Answer

Sorry, i typed 20C1*14C3 everywhere, but it's actually:
20C1*14C2. This is for all friends.

agent47 · Answer

For all enemies, this looks like it's tricky, but I could be overthinking it. Can you check the answer or not?

agent47 · Answer

aw man why did this question get closed?