There are 10 digits, 0,1,2,3,4,5,6,7,8,9

We can choose the first digit any of 9 ways (we cannot choose 0
for the 1st digit in a 9-digit number).

For each of those we can choose the 2nd digit any of 9 ways,
for there are 9 remaining digits that weren't chosen for the 
1st digit. (we can now choose 0 as one of the digits other 
than the first).

For each of those we can choose the 3rd digit any of 8 ways,
for there are 8 remaining digits that weren't chosen for the 
1st or 2nd digit.

For each of those we can choose the 4th digit any of 7 ways,
for there are 7 remaining digits that weren't chosen for the 
1st or 2nd or 3rd digit.

For each of those we can choose the 5th digit any of 6 ways,
for there are 6 remaining digits that weren't chosen for the 
1st or 2nd or 3rd or 4th digit.

For each of those we can choose the 6th digit any of 5 ways,
for there are 5 remaining digits that weren't chosen for the 
1st or 2nd or 3rd or 4th or 5th digit.

For each of those we can choose the 7th digit any of 4 ways,
for there are 4 remaining digits that weren't chosen for the 
1st or 2nd or 3rd or 4th or 5th or 6th digit.

For each of those we can choose the 8th digit any of 3 ways,
for there are 3 remaining digits that weren't chosen for the 
1st or 2nd or 3rd or 4th or 5th or 6th or 7th digit.

For each of those we can choose the 9th digit either of 2 ways,
for there are 2 remaining digits that weren't chosen for the 
1st or 2nd or 3rd or 4th or 5th or 6th or 7th or 8th digit.

Mutily all those numbers of ways together:

9×9×8×7×6×5×4×3×2 = 3265920 9 digit numbers with all different 
digits.

Edwin