Chapter 15.5, Problem 7WE

To determine

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

Answer to Problem 7WE

The number of ways to are $1024$ .

Explanation of Solution

Given information:

There are 10 true false questions and each question needs 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 needs to be answered.

There are 2 choices for first question. Either the answer can be true or false.

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

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

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,

  $\begin{array}{c}2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2=2^{10}\\ =1024\end{array}$

Thus, the number of ways to answer all 10 question are $1024$ .