RE: Brainsteem Mathematics Challenges: Quarter Finals Quirk by drdawud

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· @drdawud · (edited)
$0.12
The way I see it, we can work it out like this:

Suppose an English team (Man U) is drawn for spot "A"... then the possibility of them facing another English team (Arsenal) is (1/7).  Arsenal's only chance to be paired with Man U is naturally in spot B.

Suppose next, an Spanish team (Sevilla) is drawn for spot "C".  The probability that they won't be paired with an Spanish team (Madrid) is 3/5.

For the remaining Spanish team the proability that they dont' get put against a Spanish teams is 2/3.

Multiplying these numbers gives:  6/105 = 2/35 or about 5.7%, not an impossibility, but a more-likely-than-not scenario!

Note:  Alternatively, we could calculate the probability by similarly placing Sevilla in slot C, then calculating that Madrid is placed in a favorable position: 4/5.  Similarly, the remaining team has a 1/2 chance of being placed in a favorable position.  This gives 2/35, the same result as above.
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@rycharde ·
Haha! I guess it depends which nation's press one reads. Yes, there was also the astonishment that the 3 Spanish teams avoided each other *and* the 2 Premier League teams were paired.
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@drdawud ·
It seems a bit odd, but I suppose if you run the numbers it's not impossible.  By the way, I've posted what I hope is an interesting question on my own blog, and if you're interested, I want to invite you to take a look.
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@sammy111100 · (edited)
$0.05
Your calculations seem to be right. I got the same answer
Freely place the first british team: propbability 1 free spaces 3x2+1
British teams together: probability 1/7 free spaces 3x2
Freely place Spanish team: probability 1 free spaces 2x2+1
Second Spanish team not with the first one: probability 4/5 free spaces 1x2+1+1
Third Spanish team with neither one of the Spanish: probability 2/4=1/2

So a total of 1x1/7x1x4/5x1/2=4/70=2/35 which indeed is approximately 5,7%

I just saw it now since I was in school before. Well done!
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