Some time back in the late nineties or early 2000s, when England had four teams in the Champions League quarter-finals and someone complained in my hearing that the draw was obviously a fix because two of the English teams were drawn against each other, I quickly played about with Excel in order to add some mathematical accuracy to my counter-argument that that person was extremely stupid, and worked out that the chance of all four games being one English team and one foreign team was only twenty-two-and-six-sevenths percent.
But that figure seemed so obviously not right, because I would have thought it was exactly 25% if it was anything, that I assumed I'd done something wrong, so I never did come back with my brilliant rebuttal of the whole 'fix' calumny. However, I just did the same thing with my more advanced version of Excel, and it still only says 22.857142 recurring percent, so either I'm very consistent in doing something wrong after all these years, or the universe really is so badly aligned that the chance of all four English teams ending up in different games doesn't work out to a nice round number.
Somebody out there please do some maths, because otherwise I'm going to have to devote hours to doing the whole thing properly.
