Phone Numbers 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 these rules? That same rule applies to the exchange numbers, 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 these 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.)
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Phone Numbers 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 these rules? That same rule applies to the exchange numbers, 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 these 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.)
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
