These are counting problems. If you use a tree diagram, that is sufficient explanation by itself. However, for othermethods of counting you will need to give some explanation to justify your answer.9. A student is taking a 12-question multiple choice test. Each question has 5 choices. How many wayscan the student fill out the answer sheet so there is at least one place where two consecutive answersare the same?

Total possible ways the student can fill the answer sheet 512 , because he has 5 options in the 12 questions. Total possible ways the student can fill the answer sheet with no consecutive answers: 5.411 , Because in the first question he can answer any of the 5 options, so, in the remaining questions he can only answer 4 options to avoid choosing consecutive answers. Total possible ways the student can fill the answer sheet with at least two consecutive answers: 512 -5 . 411 = 223,169,105.

Math

Algebra

A student is taking a 12-question multiple choice test. Each question has 5 choices. How many ways can the student fill out the answer sheet so there is at least one place where two consecutive answers are the same?

A student is taking a 12-question multiple choice test. Each question has 5 choices. How many ways can the student fill out the answer sheet so there is at least one place where two consecutive answers are the same?

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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These are counting problems. If you use a tree diagram, that is sufficient explanation by itself. However, for other
methods of counting you will need to give some explanation to justify your answer.
9. A student is taking a 12-question multiple choice test. Each question has 5 choices. How many ways
can the student fill out the answer sheet so there is at least one place where two consecutive answers
are the same?

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