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| Math Central | Quandaries & Queries |
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Question from Melissa: Hello, I am looking to find out how many different combinations there are in 12 sports games. Let's say I have 12 baseball games, total 24 teams, and there can only be two results, win or lose, no ties. How many combinations can there be for 12 games? Thank-you very much. |
Hi Melissa,
For each game there are two possible results, the first team wins and the second loses or the first team loses and the second team wins. Thus if there are only 2 teams and one game there are 2 possible outcomes. If you add a second game then, regardless of the outcome of the first game there are two possible outcomes for the second game. Thus there are 2 × 2 = 22 = 4 possible outcomes if there are two games. Now add a third game. Again, regardless of the outcome of the first two games there are two possible outcomes for the third game. Thus there are 2 × 2 × 2 = 23 = 8 possible outcomes if there are three games.
This argument shows you how to determine the number of possibilities for any number of games.
Penny
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