Sum
In a test, 5 questions are of the form 'state, true or false'. No student has got all answers correct. Also, the answer of every student is different. Find the number of students appeared for the test.
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Solution
True/false questions can be answered in 2 ways either by making it true or false.
∴ each of the 5 questions can be answered in 2 different ways.
∴ total number of different sequences of answers
25 = 2 × 2 × 2 × 2 × 2 = 32
Out of these one sequence is of correct answers and no student has written all correct answers.
Hence, the maximum number of students in the class
= 32 – 1
= 31
Concept: Fundamental Principles of Counting
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