Combinations in soccer games results

dimkino

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Dec 16, 2013
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Hello all, I hope to have your support in this small problem or question...
There are 14 soccer games to play, every week.
We must predict for each of 13 games, if team A or team B, will WIN, DRAW or LOSE.
The table will look something like this, we must write an "x" over the combination we choose. Only one "x" per pair.

Ex:
1. Team A vs. Team B - W D L
2. Team A vs. Team B - W D L
3. Team A vs. Team B - W D L
...
13. Team A vs. Team B - W D L

And the last game, we must predict if the game will end 0:0, or 1:1, or 1:M, or M:1, or one of ... 15 combinations, (where M is more than 1 goal)

14. Team A vs. Team B - 0 1 M : 0 1 M


Now, the question is... How many combinations can be done, so that whatever the result of the games are, we will have at least one correct combination?
And how do you calculate it? Formula used?

Will be very gratefull for your time and help!

Thanks!!! :)
 
Last edited:
Hello all, I hope to have your support in this small problem or question...
There are 14 soccer games to play, every week.
We must predict for each of 13 games, if team A or team B, will WIN, DRAW or LOSE.
The table will look something like this, we must write an "x" over the combination we choose. Only one "x" per pair.

Ex:
1. Team A vs. Team B - W D L
2. Team A vs. Team B - W D L
3. Team A vs. Team B - W D L
...
13. Team A vs. Team B - W D L

And the last game, we must predict if the game will end 0:0, or 1:1, or 1:M, or M:1, or one of ... 15 combinations, (where M is more than 1 goal)

14. Team A vs. Team B - 0 1 M - 0 1 M


Now, the question is... How many combinations can be done, so that whatever the result of the games are, we will have at least one correct combination?
And how do you calculate it? Formula used?

Will be very gratefull for your time and help!

Thanks!!! :)
It's a very big number.

With respect to the first 13 teams, there are three possibilities for each team. And there are 15 possibilities for the last team so the answer is

\(\displaystyle 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 15 = 5 * 3^{14} \approx 23.9\ million.\)
 
Thank you JeffM, for your fast answer...
But, if we omit, the 14th game, combinations are much less, so there are chances from 1.59 millions of combinations.

There are a formula that shows this combinations? I will attach an image to understand better what I mean.
9.jpg toto 2013.jpg
 
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