Question

Given the following 10-digit phone number NYZ-ABC-XXXX, where NYZ represent the area codes, ABC represent the exchange codes and XXXX represent the station codes, How many possible 10-digit phone numbers are available with the following restrictions: the Area Code is 817 A cannot be 0 B and C cannot be 1 X can be any digit 0-9

Answer 1

There are 6,561,000 possible 10-digit phone numbers available with the specified restrictions on the area, exchange, and station codes.

Step-by-step explanation:

To calculate how many possible 10-digit phone numbers are available with the given restrictions, we can use combinatorics. Starting with the area code, which is defined as 817, we need not consider its permutations since it has been pre-set. The next set of digits is the exchange code ABC. The number A cannot be 0, giving us 9 possible values (1-9). B and C cannot be 1, so they each have 9 possible values (0 and 2-9). For each of the last four station code digits XXXX, X can be any digit from 0 to 9, giving us 10 possibilities for each position.

Therefore, the total number of possible phone numbers is calculated by multiplying the possibilities together:

• 9 possibilities for A (cannot be 0)
• 9 possibilities for B (cannot be 1)
• 9 possibilities for C (cannot be 1)
• 10 possibilities for each of the four Xs

The product of these possibilities gives us the total number of potential phone numbers:

9 (for A) * 9 (for B) * 9 (for C) * 104 (for XXXX)

This results in 9 * 9 * 9 * 104 = 6561 * 104 = 6,561,000 possible phone numbers.