a 7 digit phone number has a 3 digit prefix followed by 4 digits.how many different phone numbers are possible??
I assume 0 through 9 are allowed and repeats are possible. For example 000-0000 is allowed.
How many prefixes?
10*10*10 = 1,000
how many digits
10*10*10*10 = 10,000
so 10^3 * 10^4 = 10^7 = 10 million
I guess that is why they needed area codes.
7!=1*2*3*4*5*6*7=... (combinatoric)
To find the number of different phone numbers possible, we need to consider the number of options for each digit of the phone number.
In this case, we have a 7-digit phone number with a 3-digit prefix followed by 4 digits.
For the 3-digit prefix, we have 10 options for the first digit (0 - 9, inclusive), 10 options for the second digit, and 10 options for the third digit. Therefore, the total number of options for the 3-digit prefix is 10 * 10 * 10 = 1000.
For the 4 digits following the prefix, we also have 10 options for each digit. Therefore, the total number of options for the 4 digits is 10 * 10 * 10 * 10 = 10,000.
To find the total number of different phone numbers, we multiply the number of options for the prefix by the number of options for the remaining digits: 1000 * 10,000 = 10,000,000.
Therefore, there are 10,000,000 different phone numbers possible with a 7-digit phone number where the first 3 digits represent the prefix and the remaining 4 digits can be any number from 0 to 9.