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?

Denote the probability by p.

p=n/d , where

n(umerator)=8*7*6*5 (1st sup. team has 8 choices, 2nd 7 etc)

d(enominator)= 8^4 (independent choice -each team in one of the houses) 

p=n/d =7*6*5/(8^3)=105/256  i.e. slightly over 40%

Posted by Ady TZIDON on 2014-08-26 11:25:57