How many four digit numbers are there, with no digit repeated?

The digits of the four digit number can be formed using the digits 0, 1, 2, 3, ...9 (Totally 10 digits including '0').

But since a number cannot start with '0' the 1000th digit can be filled using any digit from 1 to 9 (i.e. 9 digits). Hence it can be filled in 9 ways. 

And the 100th place can be filled using any digit from 0 to 9(i.e. 10 digits). Since already one digit is used in the 1000th place the only 9 digits can be used.  Hence it can also be filled in 9 ways. 

Similarly the 10th place and the unit place can be filled in 8 and 7 ways respectively. 

Therefore the total number of ways = 9 x 9 x 8 x 7 = 4536.

Therefore there are 4,536 number of four digit numbers which are not repeated are there.