In a 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 :
- (a) 10
- (b) 18
- (c) 26
- (d) 32 ✓ UPSC's answer
Why the answer is (d)
• Each of the five questions can be answered in 2 ways (T or F).
• The number of different answer sequences is 2 × 2 × 2 × 2 × 2 = 32.
• No two candidates may give the same sequence, so at most 32 candidates are possible.
• Hence 32, option (d).
Why the other options are wrong
- (a) 10
- 10 is less than the total number of possible unique sequences (32), so it is not the maximum.
- (b) 18
- 18 is less than the total number of possible unique sequences (32), so it is not the maximum.
- (c) 26
- 26 is less than the total number of possible unique sequences (32), so it is not the maximum.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2016, held on 7 August 2016. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.