Chapter 15.5, Problem 8WE

To determine

To calculate: The number of ways to answer 10 true false question.

Answer to Problem 8WE

The number of ways to are $59049$ .

Explanation of Solution

Given information:

There are 10 true false questions and each question need not to be answered.

Formula used:

Fundamental counting principle states that if there are m ways to make a selection and n ways to make a second selection then there are $m\times n$ number of ways in which two selection can be made.

Calculation:

Consider the provided information that there are 10 true false questions and each question need not to be answered.

There are 3 choices for first question. Either the answer can be true or false or can be unanswered.

Similarly for second question there are 2 choices for first question. Either the answer can be true or false or can be unanswered.

That is for each question there are 2 choices for first question. Either the answer can be true or false or can be unanswered.

There are 10 questions.

Recall that Fundamental counting principle states that if there are m ways to make a selection and n ways to make a second selection then there are $m\times n$ number of ways in which two selection can be made.

Therefore, the number of ways to select are,

  $\begin{array}{c}3\times 3\times 3\times 3\times 3\times 3\times 3\times 3\times 3\times 3=3^{10}\\ =59049\end{array}$

Thus, the number of ways to answer 10 question are $59049$ .