Number of 4-digit numbers having different digits. How many four-digit positive integers are there such that all digits are different?
For a valid $4$-digit number, the Highest Significant digit will be among $1\cdots9$ so can have $9$ values

From the next onwards, they can assume $0\cdots 9$ excluding the ones already selected 

So, the number of combinations will be $$9\cdot9\cdot8\cdot7$$
Allowing for a zero first digit

10 * 9 * 8 * 7

10 possible options for the first digit, 9 remaining options for the second digit, 8 remaining options for the third digit ...