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Math Help - Tricky Combinations Question - Am I doing it right?

  1. #1
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    Unhappy Tricky Combinations Question - Am I doing it right?

    I hate to be asking so many questions one after another but I can't seem to figure any of them out.

    Q: A field-hockey team played 7 games and won 4 of them. There were not ties.

    a) How many arrangements of the 4 wins and 3 losses are possible? Is the solution 7C4? It matches the answer which is 35.

    b) In how many of these arrangements would the team have at least 2 wins in a row?

    I'm stumped on this one....

    Thanks a lot!
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  2. #2
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    Hello, MATHDUDE2!

    Q: A field-hockey team played 7 games and won 4 of them.
    There were no ties.

    a) How many arrangements of the 4 wins and 3 losses are possible?

    Is the solution _7C_4 ? . . . . Yes!

    Seven games were played: . _ _ _ _ _ _ _

    In how many ways can we place the four W's?

    Choose 4 of the 7 games: . _7C_4 \:=\:35 ways.



    b) In how many of these arrangements would the team have at least 2 wins in a row?

    The only way in which the team does not have two wins in a row is:
    . . W L\:WL\:WL\:W . . . one way.

    Therefore, there are: . 35 - 1 \:=\:34 ways to have at least 2 wins in a row.

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  3. #3
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    Thanks for the response! This really clarified my understanding!
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