Question

A question paper had ten questions. Each question could only be answered as True (T) or
False (F). Each candidate answered all the questions. Yet, no two candidates wrote the
answers in an identical sequence. How many different sequences of answers are possible?
1) 20 2) 40 3) 512 4) 1024

Answer 1

Option 4) 1024 will be the right answer

Explanation:

• As we know, that a true annf false question has two possibilities. Either being true or false.
• The questions described that there are ten number of questions in total.
• Hence, two calculate the possibilities we know, $2^{10}$ , will give 1024 as the answer.
• Hence, there are 1024 different sequences of answers that can be possible.

Answer 2

Given : A question paper had 10 questions

Each question could only be answered as True or False.  

To Find : How many candidates wrote the exam

Solution:

Number of Questions =10

Answer options for each Question = 2  True or False.

Each answer can be written in 2 ways

Total number of ways = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2

= 2¹⁰

= 1024

Hence maximum  1024  students can answer in such a way that no two candidates wrote the answers in an identical sequence.

Number of students  = 1024

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