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Math Help - how many different outcomes question

  1. #1
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    how many different outcomes question

    I want to find out all the different combinations of 16 different sets, for example here is what my set looks like

    a-b
    a-b

    for just two sets i figure there are 4 different outcomes

    outcome 1.
    a-b
    a-b

    outcome 2.
    b-a
    b-a

    outcome 3.
    b-a
    a-b

    outcome 4.
    a-b
    b-a
    which would be 2 x 2 =4, and if its 4 sets
    a-b
    a-b
    a-b
    a-b
    I get 16 different outcomes 4 x 4=16
    but for 16 sets I would think it would just be 16 X 16=256
    but when writing out all the possible outcomes it seems like it would be more than that. What would be a good formula to figure out all the different outcomes or even what would the answer be, thanks
    Last edited by catskill; September 26th 2006 at 05:30 PM.
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  2. #2
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    Lexington, MA (USA)
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    Hello, catskill!

    If no one is responding, it's because we can't figure out what you're saying . . .


    I want to find out all the different combinations of 16 different sets.
    Exactly how are these "combinations" formed?
    It seems that we have 16 objects.
    Are we taking them one at a time, then two at a time, then three at a time, etc. ?


    For example here is what my set looks like:

    a-b
    a-b
    Just what is this set?
    Are there two objects in the set ... both of them "a-b"?
    Is that really a subtraction?

    We might be able to help if you gave us the original problem.

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  3. #3
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    Sorry, looking at it now it does look confusing, I was trying to turn a outcome issue into a math type question and probably confused things. Here my original question.

    Their are 14 games football games played on sunday
    ex.
    CARDINALS vs FALCONS
    VIKINGS vs BILLS
    SAINTS vs PANTHERS
    COLTS vs JETS
    49ERS vs CHIEFS
    COWBOYS vs TITANS
    CHARGERS vs RAVENS
    DOLPHINS vs TEXANS
    LIONS vs RAMS
    PATRIOTS vs BENGALS
    BROWNS vs RAIDERS
    REDSKINS vsSEAHAWKS
    PACKERS vs EAGLES
    patriots vs broncos


    I have a pool at work where you pick all the winners for the week, i just wanted to know how many different outcomes their are and how i can find this out. If it was 3 games i get 9 different outcomes but for 14, i thought i would just multiply 14 by 14 and get 196 different outcomes but i think their are even more. What way can i get this answer, thanks.
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  4. #4
    MHF Contributor

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    Just consider your first three examples.
    CARDINALS vs FALCONS
    VIKINGS vs BILLS
    SAINTS vs PANTHERS
    There are only eight possible outcomes not nine.
    C V S
    C V P
    C B S
    C B P
    F V S
    F V P
    F B S
    F B P
    That is 2^3.
    So with 14 matches there are 2^14 possible outcomes.
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  5. #5
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    Thanks, and by 2^14 u mean 2x2x2x2x2x2x2x2x2x2x2x2x2x2 right?
    One more question
    with these teams
    bills vs lions
    falcons vs saints
    jags vs pats

    and if their was 3 outcomes per game example
    bills-win
    lions-win
    bills/lion-tie

    how many different outcomes, for this i get 27 for all 3 games, is this right.
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