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Combinatorics question

  1. Apr 21, 2014 #1
    1. The problem statement, all variables and given/known data

    You have got 10 multiple choice questions with 3 possible choices per question. What is ur chance that you will have 5 answers correct?

    So the chance for a correct answer per question is 1/3 and for an uncorrect answer per question is 2/3.

    3. The attempt at a solution

    correct solution:

    10 nCr 5 * (1/3)^5 * (2/3)^5 = 896/6561

    (with 10 nCr 5 = combination with n= 10 and k = 5 )

    I don't know how to get to the solution.

    THank u
     
  2. jcsd
  3. Apr 21, 2014 #2

    Curious3141

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    Homework Helper

    The expression is a simple application of Binomial probability. The final answer is just a simplification by cancellation of common factors.

    You first *choose* 5 questions that you get right. The other 5 are automatically decided by elimination. Then you figure out the probability of getting the 5 that you chose right and the other 5 wrong. Can you now see why the expression has that particular form?
     
  4. Apr 21, 2014 #3
    thank u
     
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