For a set of 6 MCQ questions in an interview which had four choices, none of the candidate...
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For a set of 6 MCQ questions in an interview which had four choices, none of the candidate had written all correct answers and no candidates gave the same sequence. If everyone attempted all the 6 questions, how many candidates who attended the interview?
Show answer & explanation
Each of 6 questions has 4 choices, giving 4^6 = 4096 total possible answer sequences. Since no candidate got all answers correct (excluding 1 perfect sequence) and no two candidates had the same sequence, the maximum number of candidates is 4096 - 1 = 4095.
Step-by-step Derivation:
Step 1: Calculate total possible answer sequences for 6 questions with 4 choices each.
Total sequences = 4^6 = 4,096
Step 2: Apply the constraint that none of the candidates answered all questions correctly.
This eliminates exactly 1 sequence (the all-correct answer key).
Valid sequences = 4,096 - 1 = 4,095
Step 3: Interpret 'no candidates gave the same sequence'.
This means each candidate must have a unique answer sequence.
Maximum candidates = Maximum unique (non-perfect) sequences = 4,095
Answer: 4095 ways