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?
- A.20
- B.40
- C.512
- D.1024
▶ Answer & Explanation
Correct answer: D. 1024
For each of the ten questions, there are two independent choices: True or False. Since every question must be answered, the total number of unique sequences of answers is found by multiplying the number of choices for each question together. This is a fundamental principle of counting, where the total number of possibilities is the product of the number of options at each stage. Therefore, for 10 questions, each with 2 options, the total number of distinct answer sequences is 2 multiplied by itself 10 times, which equals 2^10.
Source: UPSC gs1 2010