Question:
How many 4-digit numbers are there, when a digit may be repeated any number of times?
Solution:
To find: Number of 4 digit numbers when a digit may be repeated any number of times
The first place has possibilities of any of 9 digits.
( 0 not included because 0 in starting would make the number a 3 digit number.)
The second place has possibilities of any of 10 digits.
The third place has possibilities of any of 10 digits.
The fourth place has possibilities of any of 10 digits.
Since repetition is allowed.
So there are $9 \times 10 \times 10 \times 10=9000$ 4-digit numbers when a digit may be repeated any number of times.