Hi Jin,

Suppose you have 1 game and using your notation the team are represented by 0-1 and the possible outcomes are

0
1

so there are 2 possible outcomes.

Suppose you have 2 game and using your notation the teams are represented by 0-1, 2-3. 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

0-2
0-3
1-2
1-3

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 0-1, 2-3, 4-5. 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

0-2-4
0-3-4
1-2-4
1-3-4
0-2-5
0-3-5
1-2-5
1-3-5

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