In order to ensure that one forecast is correct, how many
different forecasts must be made of 5 football games?
Answer: 3x3x3x3x3 =
3⁵ = 243. We will have to consider each game separately, because each game may
be won, lost or drawn by one of the teams. Therefore there are three
possibilities in every game.
The first game has three possibilities and for each one of
these possibilities the second game has three possibilities. Therefore there
are 9 possible forecasts for the first two games.
For each of the 9 forecasts of the second game, the third
game has 3 possibilities, which makes it 27 forecasts and so on.
Therefore for 5 games there are 243 possibilities.
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