If I have 9 variables and three different outcomes for each variable. How many differents outcomes can there be? And what are all the outcomes? For example there are 9 games for that week and the 3 outcomes for each game that can be A:for away team T: for tie and H:for home team. How many different possibilities are there? And what are they?
We can choose the Home team any of 3 ways.
For each of those 3 ways, we can choose the away team as either of the 2
remaining teams. That 3×2 or 6 ways to choose the home team and
the away team.
For each of those 6 ways we can choose the home and away teams, there are
3 ways the score can turn out. That 6×3 or 18 ways to choose the home team and
the away team and the game can turn out.
Here are those 18 ways. The teams are A, B, and C.
Home team Away team Winner (or T for tie)
1. A B A
2. A B B
3. A B T
4. A C A
5. A C C
6. A C T
7. B A A
8. B A B
9. B A T
10. B C B
11. B C C
12. B C T
13. C A A
14. C A C
15. C A T
16. C B B
17. C B C
18. C B T
Edwin