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Math Help - Combinations/Permutations

  1. #1
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    Combinations/Permutations

    Hi,

    This will probably be very easy for most people on this site but i have no clue.

    I am trying to work out how many combinations there are for ten events each with three possible outcomes.

    Example:If you take 10 football matches each having three outcomes e.g home win,draw,away win, how many possible outcomes are there for all mathches and outcomes.

    I was told it might be 10 to the power of 3 but not sure and dont know how to work that out anyway.

    Thankyou in advance
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  2. #2
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    Quote Originally Posted by redredneck View Post
    Hi,

    This will probably be very easy for most people on this site but i have no clue.

    I am trying to work out how many combinations there are for ten events each with three possible outcomes.

    Example:If you take 10 football matches each having three outcomes e.g home win,draw,away win, how many possible outcomes are there for all mathches and outcomes.

    I was told it might be 10 to the power of 3 but not sure and dont know how to work that out anyway.

    Thankyou in advance
    3^{10}.

    Make the pigeonhole principle your friend.
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  3. #3
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    Hi,

    Cheers for that but i dont know how to do this,could you please explain how i work out?

    Thankyou
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  4. #4
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    Dubai, UAE
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    Perm/Comb

    There are 3 outcomes for the first match.
    3 outcomes for the second.
    3 outcomes for the third.
    .
    .
    .
    3 outcomes for the tenth.

    So, the number of possible outcomes = 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 =  3^{10} .

    I hope that makes it clear.

    me07.
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