Question

How many phone numbers are possible in the (770) area code if: For the form ABC-XXXX, A is restricted to numbers 2-9. B, C, and X can be any digit 0-9. Also, the number 867-5309 is not used.

a. 6,999,999 c.7,999,999
b. 7,000,000 d.8,000,000

Answer 1

c.7,999,999

Explanation:

The phone number is of the form ABC - XXXX

A can be any number from 2 - 9. This means number of possible values for A are 8.

The rest of the places B,C and X can be any digit from 0 - 9. This means there are 10 possible values for each of these.

Since, value to A can be assigned in 8 ways, and to the rest of the 6 positions in 10 ways, according to the fundamental rule of counting, the total number of possible phone numbers that can be formed will be equal to the product of all the individual ways:

Total possible phone numbers = 8 x 10 x 10 x 10 x 10 x 10 x 10

Since, 1 of the given number: 867-5309 is not used, the total possible phone numbers will be:

Total possible phone numbers =
`8 * 10^(6) - 1 = 7999999`

Hence, option C: 7,999,999 give the correct answer.