How many 4-digit numbers are there when a digit may be repeated an number of times?

Explanation

In a 4−digit number, 0 cannot be placed at the thousand's place.


So, thousand's place can be filled by any digit from 1 to 9 in nine ways.


Now, each of hundred's, ten's and one's places can be filled by any of the digits from 0 to 9 in ten ways.


So, the required number of numbers =`(9xx10xx10xx10)=9000`.