@engineer,
Number of required meetings = 12*11/2 = 66 meetings
Number of possible meetings in one party first night = 4*3/2 = 6
Number of possible meetings in one party other nights = 4*3/2 - 1 = 5
Number of parties first night = 3
Number of parties other nights = 3*3 = 9
Total number of possible meetings first night = 6*3 = 18 meetings
Total number of possible meetings other nights = 5*9 = 45 meetings
Total number of possible meetings = 45+18 = 63 meetings