Maths geniuses...

Factual Questions
1

In the upcoming soccer World Cup, there are 8 groups of 4 teams in the first rounds of the tournament. What I would like to know is, how many different possible combinations could occur in terms of the teams that win their group? Eg, one combination would be:

Group winners:

France
Spain
Brazil
Portugal
Germany
Argentina
Italy
Russia

How many combinations all up?

Thanks in advance.

2

Can a maths mediocrity join in? There are 4 possible choices for each of 8 groups. Thus the total is 4[sup]8[/sup] = 65,536 possible combinations.

3

Yes, but what about the two favarourites? 2 to the power of 8?

4

I’m pretty good at math and if I understand the question properly, I’d support Jabba’s answer of 65536.

5

If you mean how many combinations of qualifiers are there, there are two answers.

  1. If we ask simply which teams qualify: there are 4C2 = 6 ways of choosing the 2 qualifiers from each group. The total no. of combinations is then 6[sup]8[/sup] = 1,697,616.
  2. If we are interested in the positions of each qualifier: the winner of each group can be chosen in 4 ways; the runner-up can then be chosen in 3 ways. There are thus 4*3 = 12 ways of coosing first and second place in each group. The total no. of such combinations is now 12[sup]8[/sup] = 429,981,696
6

My last post was in response to vance, BTW.

7

Thanks Jabba.

8

Jabba BTW?

9

BTW = By the way.