Cong Han’s Post

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Statistician at Astellas Pharma

Among the 16 clubs that move on to the next stage of UEFA Champions League, all 4 Spanish clubs and both English clubs won their group and all 3 Italian clubs finished as runners-up. Thus, apart from the constrains that no teams from the same group can play each other, the only additional constraints are induced by German clubs in that neither Bayern nor Dortmund can be drawn against Leipzig in the round of 16. Based on the application of rook polynomials (https://lnkd.in/gVq92yXi), one can see that the rook polynomial for this situation is (1+x)^5*(1+5x+5x^2+x^3), which implies a total of 10595 possible drawing outcomes. Out of these 10595 possible outcomes, 1501 would involve Man City playing Inter. An interesting question is how to derive this without resorting to brute force enumeration…

What is the probability of this exact same Champions League draw?

What is the probability of this exact same Champions League draw?

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