For a set of five true/false questions, no student has written all correct answers, and no tow students have given the same sequence of answers. What is the maximum number of students in the classes, for this to be possible?

Options

A. 9
B. 32
C. 31
D. 24

Answer

C

Explanation

Since a true/false type question can be answered in 2 ways either by marking it true or false. So, there are 2 ways of answering each of the 5 questions. So,
Total number of different sequences of answers
`=2xx2xx2xx2=2^(5)=32`.
Out of these 32 sequences of answers there is only one sequence of answering all the five questions correctly. But, no student has written all the corrent answers and different stundents have given different sequecnes of answers. So,
Maximum number of students in the class
= Number of sequences except one sequence in which all answers are correct =32-1=31