Solution 1. It is easy to check that the number of all possible matchings of the 8 teams is 184.108.40.206=105.
The number of those cases when the opponents of the Hungarian teams are all foreign is 5.4.3=60.
The requested probability is .
Solution 2. Denote the three Hungarian teams by A, B and C. Team A has 7 possible opponents. Therefore, the probablility that the opponent of team A is team B, is exactly 1/7.
The same holds for the pairs A,C and B,C.
The three wrong cases are pairwise distinct and all remaining cases are good. Therefore the requested probablity is