This might be too complicated or fairly easy?

Jul 2009
Bit of background to the problem.
I am a member of the Arcani clan that play the game called the Empire total war. The problem that I will present to the forum, will be related to a tournament that we are going to have.

Here is the situation.(Wink)

Just bare with me ok. I appreciate your time and hopefully it will be a nice challenge for you guys.

We have 2 teams.
Team A and Team B.
These teams will play five games, first team to win three will advance.

Here are the rules(most important into calculating or solving this prob.)

Each team could pick one faction(out of ten) and in each game 4 factions will be chosen but no faction can be repeated in each game.

My math background is.. have taken Calculus classes.

Here is what i have so far.(maybe have nothing do with the prob (Nerd))
Team A ----- Team B
Game 1 10! 9! Vs 8! 7! first guy on team has 10 factions to choose
Game 2 9! 8! Vs 7! 6!
Game 3 8! 7! Vs 5! 4!
Game 4 7! 6! Vs 5! 4!
Game 5 6! 5! Vs 4! 3!

Here is the scenario that brought up this problem.

10 Factions: USA, Dutch, Russia, Prussia, France, Ottoman, India, Poland,Sweden and Spain.

Team A === Team B
Game 1 France + Prussia Vs Dutch+ USA
Game 2 Spain + Russia Vs Poland+Sweden
Game 3 Dutch + USA Vs Spain + Russia
Game 4 Poland +Sweden Vs France+Prussian
Game 5 Ottoman+India Vs ?*

?*: At this point Team B can't pick either ottoman or India because no two team can have the same faction or repeated faction.All other 8 factions are used by both teams but correctly according to the rules. At the last game, there both left with two same factions to choose from, so that's the problem.

So could this problem arise in the fourth or third game?

Thanks for All you help, We really appreciate it.
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