I found this question on gre forum, it's answer was given by this expression:
$9\cdot9\cdot8\cdot7\cdot6$ which I heard in school as well.
What I tried to do was:
for numbers from index $4$ to index $1$, we can use any of the $10$ numbers $(0-9)$ once so I got this result, $10C4\cdot4$! Now for the first index, it can be not $0$ and $4$ less number or $3$ less number to choose from depending upon whether we are selecting $0$ or not.
I know it is wrong, what Can anyone point out what is wrong with this approach?