A multiple choice exam contains 10 questions. There are four possible answers fo

Question

A multiple choice exam contains 10 questions. There are four possible answers for each question. (a) How many ways can a student answer the questions on the exam if every question is answered? (b) How many ways can a student answer the questions on the exam if the student can leave answers blank? (c) Assuming that there is only one correct answer to each question, and assuming that a student does not leave any questions blank, how many of the possibilities from part (a) of this question will earn the student a 70% or higher on the exam if all questions are weighted equally.

Explanation / Answer

A)Number of ways a student can answer the question on the exam if every question is answered=410

B)Number of ways a student can answer the question on the exam he can leave blank=510

Because we can treat leaving the question as one more option so we have total 5 options to answer.

C) To get 70 % student needs to give 7 correct answers

so now number of way to choose to the 7 correct answers out of the 10 question=10C7

now think about the remaining 3 question

number of ways to answer the remaing 3 question=43

So total number of ways to get exact 70 % = 10C7 *43

TO get 80 % ,student need to give 8 correct answers

so now number of way to choose to the 8 correct answers out of the 10 question=10C8

now think about the remaining 2 question

number of ways to answer the remaing 2 question=42

So total number of ways to get exact 80 % = 10C8 *42

TO get 90 % ,student need to give 9 correct answers

so now number of way to choose to the 9 correct answers out of the 10 question=10C9

now think about the remaining 1 question

number of ways to answer the remaing 1 question=41

So total number of ways to get exact 90 % = 10C9 *41

TO get 100 % ,student need to give all answers correct

so now number of way to choose to the 10 correct answers out of the 10 question=10C10

so now total number of ways to get at least 70 %= 10C7 *43 +10C8 *42 +10C9 *41 +10C10

so the number possibillities to get 70 % or higher on exam =10C7 *43 +10C8 *42 +10C9 *41 +10C10

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