How many 9-digit numbers of different digits can be formed?

Explanation

The ten-crore's place of a 9-digit number cannot be 0.
So, this place can be filled up by any of the digits from 1 to 9. So, there are 9 ways of filling the ten-crore's place.
The crore's place can now be filled with 0 or any of the remaining 8 digits. Thus, there are 9 ways of filling it.
The ten-lakh's place can now be filled with any of the remaining 8 digits. Thus, there are 8 ways of filling it.
Similarly, we can fill lakh's place in 7 ways, ten thousands's place in 6 ways, thousand's place in 5 ways, hundred's place in 4 ways, ten's place in 3 ways and unit's place in 2 ways.
Hence, by the fundamental principle of multiplication, the required number of numbers `=(9xx9xx8xx7xx6xx5xx4xx3xx2) = 3265920.`