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Math Help - Pairing Senators

  1. #1
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    May 2009
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    Pairing Senators

    Problem:
    There are 30 senators in a senate. For each pair of senators, the two senators are either friends of each other or enemies of each other. Every senator has exactly six enemies. Every three senators form a committee. Find the total number of committees whose members are either all friends or all enemies of each other.
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  2. #2
    Newbie
    Joined
    May 2009
    Posts
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    So far I have reached to this solution:
    1) There are total 30C2 pairs. = 435
    2) If every senator has 6 enemies then 30 senators will have total 30*60/2 enemies pairs (removing double counted ) = 90
    3) Total friend pairs are 435 - 90 = 345

    For choosing committees, we have to choose to choose 3 pairs from 90 an then 3 pars from 345 such that each node of pairs is shared with another node. But how, can't get this.

    Any other way to look at this problem?
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