In a test that has 5 true/false questions, no student has got all correct answers and no sequence of answers is repeated. What is the maximum number of students for this to be possible?
For a set of 5 true/false questions, each question can be answered in 2 ways.
∴ By using the fundamental principle of multiplication, the total number of possible sequences of answers = 2 × 2 × 2 × 2 × 2 = 32
Since no student has written all the correct answers
∴ Total number of sequences of answers given by the students in the class = 32 − 1 = 31
Also, no student has given the same sequence of answers.
∴ Maximum number of students in the class = Number of sequences of answers given by the students = 31