10000 different phone numbers are possible for a particular prefix if repetion of digits is allowed
5040 different phone numbers are possible for a particular prefix if repetion of digits is not allowed
Solution:
Given that,
A seven digit phone number consists of a three-digit prefix followed by four digits
We have to find the different phone numbers are possible for a particular prefix
For a paricualr prefix, there are four digits
Total numbers from 0 to 9 are 10
Therefore,
Different ways for phone number for particular prefix:
If repetition is allowed:
Different ways = 10 x 10 x 10 x 10 = 10000 ways
If repetition is not allowed then:
Different ways = 10 x 9 x 8 x 7 = 5040 ways