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Math Help - Permutations

  1. #1
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    Talking Permutations

    Hi , i am kinda weak at permutations nd ve been breakin me head lately over this problem ... can u help me with this

    Find the number of ways in which a student can attempt a exam, such that he answers at least two questions out of a total of 150 questions in the exam , given each question has four options .
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  2. #2
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    Having 150 questions with four options each means that there 4^{150} ways to answer the complete test.
    There are 3^{150} ways to answer the questions getting none correct.
    To get exactly one correct: we choose one of the 150 and answer the other 149 incorrectly.
    There are \left( {150} \right)\left( {3^{149} } \right) ways to do that.
    To answer at least two correctly is the opposite of none or exactly one.
    Thus 4^{150}  - \left[ {3^{150}  + \left( {150} \right)\left( {3^{149} } \right)} \right].
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