In question paper there are five questions to be attempted and answer to each question has two choices - True (T) or False (F). It is given that no two candidates have given the answers to the five questions in an identical sequence. For this to happen the maximum number of candidates is:
- A10
- B18
- C26
- D32Correct
Explanation
To find the maximum number of candidates such that no two have an identical sequence of answers, we need to calculate the total number of possible ways to answer the five questions.
Each of the five questions has 2 choices (True or False). According to the fundamental principle of counting, if there are n questions and each question has k choices, the total number of distinct sequences is k raised to the power of n.
In this case, there are 2 choices for each of the 5 questions. Therefore, the total number of unique sequences is: 2 multiplied by 2 multiplied by 2 multiplied by 2 multiplied by 2, which equals 2 to the power of 5.
2 to the power of 5 is 32.
Since each candidate must have a unique sequence, the maximum number of candidates possible is 32. If there were 33 candidates, at least two would have to share the same sequence.
The correct answer is D.
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