Chapter 12.6, Problem 11PPE

a.

To determine

To calculate: The number of choices for the first digit. Also, after the first digit.

Answer to Problem 11PPE

The choices for first digit is 8 and for other digits it is 10.

Explanation of Solution

Given information:

A seven-digit telephone number can begin with nay digit except 0 or 1. There are no restrictions on digits after the first digit.

Formula used:

For any positive integer $n$, the expression $n$ factorial is written as $n!$ and is the product of integers from n down to 1.

Calculation:

According to the question,

The number of digits are - $0,1,2,3,4,5,6,7,8,9.$

This implies we have total $10$ number numbers that can be used to form a seven digit telephone number.

Excluding $0\text{ and }1$ , we get 8 choices for the first digit.

For second digit we have 10 choices and the rest of numbers.

Hence, total choices for first digit is 8 and for further numbers it is 10.

b.

To determine

To calculate: The number of ways seven-digit telephone numbers are possible.

Answer to Problem 11PPE

The number of wyas are $80,00,000$ .

Explanation of Solution

Given information:

A seven-digit telephone number can begin with nay digit except 0 or 1. There are no restrictions on digits after the first digit.

Formula used:

For any positive integer $n$, the expression $n$ factorial is written as $n!$ and is the product of integers from n down to 1.

Calculation:

According to the question,

The number of digits are - $0,1,2,3,4,5,6,7,8,9.$

This implies we have total $10$ number numbers that can be used to form a seven digit telephone number.

Excluding $0\text{ and }1$ , we get 8 choices for the first digit.

For second digit we have 10 choices and the rest of numbers.

Therefore ,

  $\begin{array}{l}=8\times 10\times 10\times 10\times 10\times 10\times 10\\ =80,00,000\end{array}$

Hence, the number of ways are $80,00,000$ .