Et tu, Brute ....

Suppose a company's board of directors is composed of \(20\) individuals. Each of these individuals has precisely \(6\) enemies on the board, the remaining members being friends. (Being enemies or friends is not a one-sided affair, i.e., any two board members are either enemies of one another or friends of one another.)

In how many ways can a \(3\) member subcommittee be formed such that its members are either all friends or all enemies?

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