Chapter 9.4, Problem 70E

(a)

To determine

To calculate:

The number of calls made by the telemarketer

Answer to Problem 70E

The number of calls made by the telemarketer is ${10}^7$ .

Explanation of Solution

Given information:

Phone number of $7$ digits

Calculation:

Consider the following reasoning assumptions:

First position: any one of the $10$ numbers

Second position: any one of the $10$ numbers

Third position: any one of the $10$ numbers

Seventh position: any one of the $10$ numbers

So, the required number of possible calls is estimated as:

  $\begin{array}{l}N=10\cdot 10\cdot 10\cdot 10\cdot 10\cdot 10\cdot 10\\ N={10}^7\end{array}$

(b)

To determine

To calculate:

The number of possible different calls which begins $7$ or $6$ made by the telemarketer

Answer to Problem 70E

The number of possible different calls which begins $7$ or $6$ made by the telemarketer is $2\cdot {10}^6$ .

Explanation of Solution

Given information:

Phone number begins $7$ or $6$

Calculation:

Consider the following reasoning assumptions:

First position: any one of the begins $7$ or $6$ numbers

Second position: any one of the $10$ numbers

Third position: any one of the $10$ numbers

Seventh position: any one of the $10$ numbers

So, the required number of possible calls is estimated as:

  $\begin{array}{l}N=2\cdot 10\cdot 10\cdot 10\cdot 10\cdot 10\cdot 10\\ N=2\cdot {10}^6\end{array}$