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(A) Each of the $5$ true-or-false questions can be answered in $2$ ways (True or False).The total number of possible sequences of answers for $5$ ques

Vedclass · Accepted Answer

$31$

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(A) Each of the $5$ true-or-false questions can be answered in $2$ ways (True or False).The total number of possible sequences of answers for $5$ questions is $2^5 = 2 	imes 2 	imes 2 	imes 2 	imes 2 = 32$.There is exactly $1$ sequence that represents all correct answers.Since the problem states that no student has written all the correct answers,we must exclude this $1$ sequence from the total possibilities.Therefore,the number of valid sequences is $32 - 1 = 31$.Since no $2$ students have given the same sequence of answers,each student must have provided a unique sequence from the remaining $31$ possibilities.Thus,the maximum number of students in the class is $31$.

For a set of $5$ true-or-false questions,no student has written all the correct answers,and no $2$ students have given the same sequence of answers. What is the maximum number of students in the class,for this to be possible?

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