A seven digit phone number consists of a three-digit prefix followed

by four digits. How many different phone numbers are possible for a

particular prefix?

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