KöMaL 2008 C964

In last year's football Champions' League, it happened for the first time ever that four teams of the same country, England (Arsenal, Chelsea, Liverpool and Manchester United), qualified for the best eight. The eight teams were paired up at random, and the winner from each pair qualified for the best four. $a$) Some English football supporters wished that the English teams would not be paired together, to make it possible for all four of them to qualify for the semi-finals. What was the probability of such a pairing? $b$) Other English supporters wished that the four English teams would form two pairs, to make sure that two of them would qualify for the semi-finals. What was the probability of such a pairing? $c$) In reality, two English teams were paired together and the other two teams got non-English opponents. What was the probability of such a pairing?