Thinkhub holds a welcome party for the new term. Ten families attend this party, and each family has a father, a mother and a child.  Each father shakes hands with all the people from other families.  Each mother only shakes hands with all the fathers and children from other families.  Each child only shakes hands with all the fathers and mothers from other families.  How many handshakes occur among these $$10$$ families? 
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