Problem 3.An exam has 30 multiple choice questions. Each question has five answer choices, ofwhich exactly...

Problem 3.An exam has 30 multiple choice questions. Each question has five answer choices, ofwhich exactly one is correct. In how many different ways can a student who answers all questionsget at least 27 of them correct?

Solutions

Expert Solution

No. of way in which 27 answers are correct = (₃₀C₂₇*1)*(4*4*4) [First we select 27 questions from 30, each of them can be answered correctly in one way. Each of the remaining 3 questions can be answered incorrectly in 4 ways]

Therefore, no. of way in which 27 answers are correct = 259840

No. of way in which 28 answers are correct = (₃₀C₂₈*1)*(4*4) [First we select 28 questions from 30, each of them can be answered correctly in one way. Each of the remaining 2 questions can be answered incorrectly in 4 ways]

Therefore, no. of way in which 28 answers are correct = 6960

No. of way in which 29 answers are correct = (₃₀C₂₉*1)*(4) [First we select 29 questions from 30, each of them can be answered correctly in one way. Remaining 1 question can be answered incorrectly in 4 ways]

Therefore, no. of way in which 29 answers are correct = 120

No. of way in which 30 answer are correct = ₃₀C₃₀ = 1

No. of different ways in which student get at least 27 answers correct = 259840+6960+120+1

No. of different ways in which student get at least 27 answers correct = 266921

orchestra answered 1 year ago

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