Question

A seven digit telephone number is of the form ABC-DEFG. In one particular state, the digit ‘A' is restricted to any number between 1 and 9. The digits B and C are restricted to any number between 2 and 9. The digits D,E,F, and G have no restriction. How many seven digit phone numbers are possible with these restrictions?

Answer 1

2,520,000

Explanation:

We are told the telephone number has seven digits of the form ABC-DEFG

We are told that the digit ‘A' is restricted to any number between 1 and 9.

Between 1 and 9 means numbers in between 1 and 9. So 1 and 9 are not included.

This means the numbers include 2, 3, 4, 5, 6, 7, 8. Which means there are 7 ways to select.

We are also told that digits B and C are restricted to any number between 2 and 9

This means that the numbers are; 3, 4, 5, 6, 7, 8. It means there are 6 ways to select.

Now, we are told that digits D,E,F, and G have no restriction. Thus, there are 10 ways to select each digit.

To find the Number of seven digit phone numbers that are possible with these restrictions, we will multiply each individual number of ways for each digit.

Thus;

Probability = 7 × 6 × 6 × 10 × 10 × 10 × 10 = 2,520,000