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Math Help - number of games - counting

  1. #1
    eri
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    number of games - counting

    Bball tournament, 8 teams play eachother once
    What's the number of games in tournament?

    Aside from making a list counting out the possibilities,
    How can you quickly figure this out, and what is the reasoning behind it?

    I figured
    (8 teams) *(7 "each team can play this # teams" )* (1 game/2 teams)
    so 28 is answer, which is the same i get when making a list of all the possibilities by hand.

    but am not sure what 7 exactly refers to--
    Looks like the number of other teams each team could play against.
    What would you describe it as? (what it is called doesnt seem to "cancel out" here--but what is it called anyways)


    PLease let me know what you think !! thanx
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  2. #2
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    Eight teams playing two at a time:
    {8 \choose 2}=\frac {8!} {(2!)(6!)}=\frac {(8)(7)}{2}
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  3. #3
    eri
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    Question about Combinations

    Quote Originally Posted by Plato View Post
    Eight teams playing two at a time:
    {8 \choose 2}=\frac {8!} {(2!)(6!)}=\frac {(8)(7)}{2}

    what is (8/2) ?
    Is this Combination problem?
    where you say number of larger group n=8, number choosing "choose 2 " k=2?

    n!/(k!(n-k)!)

    But this is weird because you wouldn't think that it would be "choose 2"
    8 teams, choose 2? that's weird. or is it ,choose any 2 to play eachother

    How many different ways to chose 2 teams from 8 players!!!
    Got it!
    Or Number of different games of 2 teams that can be selected from 8 teams?
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