# Product Rule for Counting/Examples/6 Football Matches

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## Example of Use of Product Rule for Counting

Let it be understood that a football match between two teams $\text A$ and $\text B$ can end as:

- A win for team $\text A$
- A draw
- A loss for team $\text A$.

That being understood, then there are $729$ ways to predict the results of $6$ football matches.

## Proof

Each match as the above described $3$ possible outcomes.

Hence by the Product Rule for Counting, there are $3 \times 3 \times 3 \times 3 \times 3 \times 3 = 3^6 = 729$ possible ways of forecasting the result of $6$ such matches.

$\blacksquare$

## Sources

- 1953: L. Harwood Clarke:
*A Note Book in Pure Mathematics*... (previous) ... (next): $\text I$. Algebra: Permutations and Combinations: Exercises $\text I$: $10$