Chapter 15.5, Problem 11WE

To determine

To calculate: The number of ways to create a 7-digit telephone number.

Answer to Problem 11WE

The number of ways to create a 7-digit telephone numberare $20,000$ .

Explanation of Solution

Given information:

In a 7-digit telephone number first digit must be 8, second must be 5 and third must be 2 or 3.

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 in a 7-digit telephone number first digit must be 8, second must be 5 and third must be 2 or 3.

Let 7-digit telephone numberbe $\boxed{}\boxed{}\boxed{}\boxed{}\boxed{}\boxed{}\boxed{}$ .

To select the first digit there is only one option that is 8 according to the question $\boxed{1}\boxed{}\boxed{}\boxed{}\boxed{}\boxed{}\boxed{}$ .

Similarly second digit should be 5 so only 1 choice to fill it, $\boxed{1}\boxed{1}\boxed{}\boxed{}\boxed{}\boxed{}\boxed{}$ .

Third digit can be either 2 or 3 so third box can have 2 possibilities $\boxed{1}\boxed{1}\boxed{2}\boxed{}\boxed{}\boxed{}\boxed{}$ .

Since digits are available from 0 to 9 and no restriction on repetition of digits so remaining 4 boxes can be filled with 10 options each.

  $\boxed{1}\boxed{1}\boxed{2}\boxed{10}\boxed{10}\boxed{10}\boxed{10}$

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,

  $1\times 1\times 2\times 10\times 10\times 10\times 10=20,000$

Thus, the number of ways to create a 7-digit telephone number are $20,000$ .