SEARCH HOME
 Math Central Quandaries & Queries
 Question from Jin: I'm trying to make a list to view all the possibility. An example is if I have 2 games there's two outcomes (home/away) I will use number to represent the teams. 0-1,2-3 All possible out comes are 0-2,0-3,1-2,1-3 right? MY QUESTION If I have 10 games each have 2 outcomes (home/away) to win What is all possible outcome. 0-1,2-3,4-5,6-7,8-9,10-11,12-13,14-15,16-17,18-19 Could u please provide me with a list of all possible out comes Thanks you

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

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.