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In how many ways can a student answer a five question multiple choice quiz if there are four answer choices for each question and the student never makes the same choice for two consecutive answers

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barnuts

So there are a total of five questions to answer and four choices each question. The following scenario is just an example:

1st question = 4 choices (picks A)

2nd question = 3 choices (picks B, cannot pick A)

3rd question = 2 choices (picks C, cannot pick A, cannot pick B)

4th question = 2 choices (picks D, cannot pick B, cannot pick C)

5th question = 2 choices (picks A, cannot pick C, cannot pick D)

 

So the total combinations:

C = 4 * 3 * 2 * 2 * 2 = 96 combinations

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