Both answers are correct, but I did it a different way using combinatorics.

It just dawned on me that there is only one way that draw could happen:
EE, Sx, Sy, Sz, x, y and z are the other 3 teams, giving 6 combinations.

Then it was a matter of finding out how many ways any quarter-final draw can be made. That gives 8!/4!2!2!2!2! = 105 possible random draws.