Quandaries and Queries

I was hoping if you can help with a problem. The question is:

If 8 basketball games being played(no ties), which means a total of 16 teams, what are the total number of possible outcomes that can occur.

I think the answer is 64, but it doesn't seem correct, can you please verify with me what the answer really is.

Thank you
Gianni.

Hi Gianni,

I am going to use table to attempt to keep track of all the possible outcomes. First consider the situation where the is just one game. There are 2 possible outcomes, either the home team wins or the away team wins. In the table H indicates that the home team wins and A that the away team wins.

 Game 1 H A

Now add a second game. How many columns do you need to list all possible outcomes?

 Game 1 H A Game 2

The point to notice is that the result of game 2 could be either H or A so you need to double the number of columns. Thus there are 4 possible outcomes when there are 2 games.

 Game 1 H A H A Game 2 H H A A

Now a third game. Again you need to double the number of columns. For each column in the previous table that lists a possible outcome for two games, you need two columns, one with an H in the third row and another with an A in the third row. Hence there are 8 possible outcomes for 3 games.

 Game 1 H A H A H A H A Game 2 H H A A H H A A Game 3 H H H H A A A A

Can you complete the problem now?

What happens if ties are allowed?
Penny

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