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Math Help - combinations

  1. #1
    Junior Member Rachel.F's Avatar
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    combinations

    we want to up stairs with 12 steps. We can pass by to steps on once. How many ways can we up the stairs?
    Solution: 233

    Please help. I had already done but i didnt get the correct answer, only aproximations
    Last edited by mr fantastic; December 9th 2009 at 07:22 PM. Reason: Restored original question.
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  2. #2
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    Quote Originally Posted by Rachel.F View Post
    we want to up stairs with 12 steps. We can pass by to steps on once. How many ways can we up the stairs?
    Solution: 233
    We can decide to use anywhere from zero to six double steps (two at a time).
    For example: we decide to take 3 double steps: three 2ís and six 1ís.
    The number of ways we can do that is \frac{9!}{3!\cdot 6!}=\binom{9}{3}.
    So calculate  \sum\limits_{k = 0}^6 \binom{12-k}{k}
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