Chapter 8.5, Problem 23E

(a)

To determine

To find: the total number of ATM codes possible.

Answer to Problem 23E

The possible numbers of ATM codes are 100000.

Explanation of Solution

Given information:

ATM personal identification number codes typically consist of four digit sequences of numbers.

Calculation:

First digit can be any one number from 0 to 9.

Second digit can be any one number from 0 to 9.

Third digit can be any one number from 0 to 9.

Fourth digit can be any one number from 0 to 9.

The possible numbers of ATM codes are:

  $\begin{array}{l}=10\times 10\times 10\times 10\times 10\\ =100000\end{array}$

(b)

To determine

To find: the total number of ATM codes possible when the first digit is not 0.

Answer to Problem 23E

The possible numbers of ATM codes when the first digit is not zero are 9000.

Explanation of Solution

Calculation:

First digit can be any one number from 1 to 9.

Second digit can be any one number from 1 to 9.

Third digit can be any one number from 1 to 9.

Fourth digit can be any one number from 1 to 9.

The possible numbers of ATM codes when the first digit is not zero are:

  $\begin{array}{l}=9\times 10\times 10\times 10\\ =9000\end{array}$