\section*{Exercise 6 - 031016}

In the football Toto, on the betting slip, 12 matches need to be marked for which team is expected to win or if the match will end in a draw. For each match, there are three possibilities:

Team A wins, Team B wins, or a draw.

How many betting slips would someone need to fill out to ensure they have one slip with 12 correct predictions? The solution method must be justified.
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For just one game, you would need three betting slips, one for each of the possible outcomes. For two games, you would have to fill out a betting slip for every conceivable combination, which is \(3 \cdot 3=3^{2}\) possibilities. With each additional game, the number must be multiplied by three, leading to \(3^{12}=531441\) betting slips for 12 games.