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The teacher of a mathematics class has written up the final exam, but wants

the questions to be random for each student. There are 28 students in the class, and
the test has 100 questions. Each question has four possible answers.

a. After reading carefully reading the scenario, determine the number of different
final exams possible. Besides your method, are there other methods to determine
the number of outcomes?

b. For this scenario, which will work better to determine the order of the questions,
permutation or combination? Justify your answer.

c. If a student doesn’t show up to take the test, how does that affect the number of
outcomes?

d. Suppose the teacher doesn’t end up randomizing the questions on the exam. Does
this affect the number of outcomes?

e. If each question on the test had the same answer (let’s say C), what’s the probability
that students taking the test will get all the questions right? Justify your answer.

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2 answers

  1. Please see the answers for the Related Questions below.

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    Ms. Sue
  2. a.
    There are 100! final exams possible, by permuting all 100 questions.
    b. see part a.
    c. The experiment is not clearly defined, so neither is the number of outcomes.
    If the experiment is to determine the number of exams possible, the number of outcomes does not depend on the number of students.
    If the experiments is the results of the test, then yes, the number of students affects the number of outcomes (from 28 to 27)
    d. There will still be 28 outcomes.
    e. It depends on how much students have studied. Quesion did not say the students answer at random.

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