# Six-Teams Tables

There are 6 teams in the Republic of Ireland’s qualifying group for Euro 2016. Firstly, how many ways mathematically speaking, could the order of the group turn out? And, secondly if as expected, Germany tops the group and Gibraltar ends up bottom how many different ways could the group finish?

Solution: Mathematically there are 720 ways the group could finish up.

If Germany is on top and Gibraltar on bottom then there are 24 ways the group could finish.

If we consider the table from the top down:

There are six possible teams (mathematically speaking) that could top the group.

For each of these there are five teams that could be in second place.

There are 6x5 = 30 arrangements of first and second.

Extending this to all places-

There would be four possibilities for third place.

Three possibilities for fourth place.

Two possibilities left for fifth place and only one remaining possibilities for sixth.

There would be then 6x5x4x3x2x1 arrangements overall.

6x5x4x3x2x1 = 720

If we fix the top and bottom place we really are just asking how four teams can be arranged.

And that by the above reasoning is 4x3x2x1 = 24