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Possibilities: 15 t/f, one unanswered

  1. Nov 4, 2013 #1
    1. The problem statement, all variables and given/known data
    If a test consists of 15 true false questions, in how many ways can a student mark his paper if:
    a) he answers each question
    b) he leaves any one question unanswered.


    2. Relevant equations
    Multiplication of choices


    3. The attempt at a solution
    a) 2^15 Correct.
    b) 3*(2^14) Incorrect. (right answer = 245,760)
    One question has 3 choices, the rest have 2?
     
  2. jcsd
  3. Nov 4, 2013 #2
    Also made a tree diagram up to question 4, showing the pattern 3, 8, 20, 48.
     
  4. Nov 4, 2013 #3

    LCKurtz

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    Don't forget you have 15 choices for which question to not answer.
     
  5. Nov 4, 2013 #4
    Ah, okay so it's as if you make one selection out of 15, then you have 14 to pick 2 from...so

    15*(2^14)

    Thank you.
     
  6. Nov 4, 2013 #5
    My tree diagram was also set up incorrectly, correct sequence would be 1, 4, 12, 24 for up to 4 questions.
     
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