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Problem of the Week 1162

A World Cup Problem

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Suppose there are 4 superior teams among the 32 in soccer's World Cup. If the 32 are placed randomly into eight groups of 4, what is the probability that the superior teams will be in different groups?

Real-world note: FIFA actually does some seeding (details for 2014 are not completely clear yet) to avoid having top teams in the same group. So this question is an attempt to understand how critical the seeding is.

© Copyright 2013 Stan Wagon. Reproduced with permission.

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4 September 2013