how many 4 digit numbers are there with no digits repeated?

The first, that is thousands place, can be taken by any digit except 0. So, first place can be filled in 9 ways.

The second, that is hundreds place, can be taken by any digit except the one at thousands place and including zero, so this can be filled in 9 ways.

The third, that is tens place, can be filled with any digit except the two earlier, so total ways = 8.

Similarly, for ones place, total ways = 7.

So, total number of 4 digit numbers without repetition = 9 x 9 x 8 x 7= 4536