Suppose there are supporters of Brazil and supporters of Argentina. If all of them are made to stand in one line, there will be number of places where the fights can occur. Suppose the probability of the fights taking place anywhere is .
The chances of fights are similar at each place. So the average of total number of fights is
Now, we have to determine the value of . First, let's determine how many ways fights can occur in one place. There must be or for a fight to take place and how many ways other Brazil supporters and Argentina supporters can create new permutations. So the number of fights in one place is . Now the average of this value will be . That means if we divide it by the total combination, we get .
So the formula to determine is
So the answer is