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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Solution

The correct option is A 31
Question I can be answered in 2 ways. Question II can be answered Question I can be answered in 2 ways. Question II can be answered in 2 ways.
Similarly questions III, IV, V each can be answered in 2 ways. Hence, total number of possible different answers $= 2 \times 2 \times 2 \times 2 \times 2 = 32.$ There is only one sequence of all correct answers Thus, the total number of sequences are 32 -1 = 31 [Since no student has written all correct answers]
Now, as no 2 students have given the same sequence of answers, hence the maximum number of students in the class =31.

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