Question

In how many ways can a student answer 10 true-false questions if it is possible to leave a question unanswered in order to avoid an extra penalty for a wrong answer.

Answer 1

Step-by-step explanation:

There are total three possibilities for every question

You may choose “True” as an answer.

You may choose “False” as an answer.

You can leave the question “unanswered”.

Now since all the questions are independent to each other so total number of ways to answer 10 question can be found by multiplying the number of ways to answer each questions.

And since number of ways to answer 1 question is 3.

So number of ways to answer all the 10 question will be =3×3×3×3×3×3×3×3×3×3= 3^(10)=59049.

Note: Most of people will support the answer that it will be 2×2×2×2×2×2×2×2×2×2=2^(10)=1024 but it is correct only when it is mentioned that you can not leave any question unanswered.

Answer 2

Answer:

So number of ways to answer all the 10 question will be =3×3×3×3×3×3×3×3×3×3= 3^(10)=59049.