Question 1129379
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<pre>
    Imagine that for each of the 20 multiple choice questions the answers are labeled by 5 letters A, B, C, D and E  

    (5 possible answers to each question).

     By answering to each question, you mark your answer by one of the 5 letters.

     So, by answering to 20 questions, you write the word of the length 20, using one of 5 letters in each of the 20 positions.


     It is your model. The entire space of events consists of all {{{5^20}}} such words of the length 20, written in 5-letter alphabet.


         Now I am ready to answer the problem's questions.
</pre>


<U>If a student guesses on every question, find the probability of getting 12 correct</U>.


<pre>
So the student put correct marks (selects correct letter answer) in 12 cases and selects incorrect letter answers in 20-12 = 8 cases.


Giving incorrect answers, the student has 4 opportunity for each multiple choice questions, or, in all, {{{4^8}}} possibilities.


Thus the probability under the question is this value  


          {{{C[20]^8*4^8*(1/5^20)}}} = {{{((20*19*18*17*16*15*14*13)/(1*2*3*4*5*6*7*8))*(4/5)^8*(1/5)^12}}} = 8.65E-5 = {{{8.65*10^(-5)}}} = 0.0000865  (approximately).
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