A football league contains $6$ teams. During the season each team plays two matches against each other team. The result of each match is a draw or a win for one or other team. How many matches are played in the season? How many possibilities are there for full list of results for all matches played in the season?
My answer - total matches played is $\dfrac{6\times 10}{2}= 30$ or
How would I also calculate the different possibilities? Is it $6 \times 5$?
Each team plays 5 other teams twice each (one home, one away). So each team plays 10 matches. So there are 30 matches played in total (not 60, because otherwise you will double count each match).
The three possibilities for each match are a home win, an away win, or a draw.
The number of total possibilities for the full list of results $3^{30}.$