# Math Help - Permutations

1. ## 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 .

2. 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 $4^{150} - \left[ {3^{150} + \left( {150} \right)\left( {3^{149} } \right)} \right]$.