Football Game

     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.