Chapter 8.5, Problem 15E

To determine

To find: the number of ways can a 10 question true-false exam answered.

Answer to Problem 15E

The questions can be answered in 1024 ways.

Explanation of Solution

Calculation:

If an event swa $E_1$ can occur in $m_1$ ways, and an event $E_2$ can occur in $m_2$ ways then the number of in which the two events can occur is $m_1\cdot m_2$ .

Let the number of ways in which all the questions can be answered be $E$ . Consider the case of the first question. It can be answered as either true or false. That is, the number of ways in which the first question can be answered is 2. Similarly, the question from 2 to 10 can also be answered either as true or false.

Therefore, the total number of ways in which all the questions can be answered is

  $\begin{array}{c}{E}_1=2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\\ ={\left(2\right)}^{10}\\ =1024\end{array}$

The questions can be answered in 1024 ways.