Question

The 7-digit numbers in a given area code have the form ABC-XXXX, where X, B, and C can be any digit 1-9 and A is

restricted to 0-9. There are two other restrictions:
• B and C cannot both equal 1 since these values are designated for other purposes such as 911 (emergency)
and 411 (information), and
• 555-0100 through 555-0199 are reserved for fictional uses such as in television shows or movies.
According to these conditions, how many 7-digit numbers are possible in a single area
code?

Answer 1

The number of 7-digit numbers are possible in a single area code is 5248600

Explanation:

The given parameters are;

The number of digits in the area code = 7

The possible digits for X, B and C are 1 - 9 = 9 digits

The number of possible digits for A is 0 - 9 = 10 digits

Exceptions

1) B and C cannot both =

2) 555-0100 through 555-0199 are reserved for television or movies

Therefore, we have, the number of 7 digits numbers without exceptions = 10×9⁶ = 5314410 numbers

The number of the exceptions are

Exception 1) 10 × 1 × 1 × 9 × 9 × 9 × 9 = 65610 numbers

Exception 2) 555-0100 through 555-0199 = 0199 - 0100 = 200 numbers

The number of possible numbers = 5314410 - 65610 - 200 = 5248600

The number of 7-digit numbers are possible in a single area code = 5248600.