



 
Hi Jin, Suppose you have 1 game and using your notation the team are represented by 01 and the possible outcomes are
so there are 2 possible outcomes. Suppose you have 2 game and using your notation the teams are represented by 01, 23. Each of the possible outcomes from a 1 game situation can be extended to a 2 game situation by appending the possible outcomes from the second game. Thus for a 2 game situation the possible outcomes are
Thus, as you noted above there are $2 \times 2 = 2^2 = 4$ possible outcomes. Suppose you have 3 game, the teams are represented by 01, 23, 45. Each of the possible outcomes from a 2 game situation can be extended to a 3 game situation by appending the possible outcomes from the third game. Thus for a 3 game situation the possible outcomes are
Thus there are $2 \times 2 \times 2 = 2^3 = 8$ possible outcomes. Continuing in this way there are $2^{10} = 1024$ possible outcomes for a 10 game situation. To many for me but you can list them if you want. Penny 



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