A question paper had ten questions. Each question could only be answered as True (T) or False (F). Each candid

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?

Accepted Answer

The problem asks for the total number of possible sequences for ten questions, where each question has two choices, True or False.

This is a fundamental principle of counting. For each individual question, there are 2 possible outcomes. Since there are 10 questions and each is independent of the others, we multiply the number of choices for each question together.

The calculation is 2 multiplied by itself 10 times, which is 2 raised to the power of 10.

2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 equals 1024.

Therefore, there are 1024 different possible sequences of answers. Since no two candidates wrote identical sequences, this is the maximum number of unique answer keys possible.

The correct option is D.

Answer

20

Answer

40

Answer

512

Answer

1024

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?

Explanation

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