Question

current rules for telephone area codes allow the use of digits 2-9 for the first digit and 0-9 for the second and third digits. how many different area codes are possible with this rules? That same rule applies to the exchange number. which are the three digits immediately preceding the last four digits of a phone number. Given both of those rules, how many 10- digit phone numbers are possible? given that rules apply to the United States and Canada and a few islands, are there enough possible phone numbers? (assume that the combined population is about 400,000,000.

Answer 1

In this question, there are 10 digit phone number which was divided into 3-3-4 digits. Every first digit of the division should be 2-9 which mean only 8 possibilities. The other digits would be 0-9 which mean 10 possibilities. Then the calculation would be:

8*10*10   *    8*10*10    *   8*10*10*10  = 8^3 * 10*7= 512 * 10^7= 5.12 * 10^9

If you convert 400,000,000 into the scientific form it will become 4* 10^8. Since 5.12*10^9 > 4 * 10^8, then it is clear that the number should be enough