Need math help: In how many ways may the exam be completed?

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An exam consists of six true-or-false questions. Assuming that every question is answered, in how many different ways can a student complete the exam? In how many ways may the exam be completed if a penalty is imposed for each incorrect answer, so that a student may leave some questions unanswered?
Nov 15th, 2015

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Answer choice C.)  64 ways to answer True/False and 729 ways to answer true, false, or blank.

You have 6 independent individual events. each with 2 outcomes if the student answers true or false.

2^6 = 64 outcomes possible.

Now if the student has the choice to not fill in either true or false we have:

6 independent events each with 3 different outcomes.

3^6 = 729 ways.

Please let me know if you need any clarification. I'm always happy to answer your questions.
Nov 15th, 2015

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