Since the smallest digit is 0 and the largest
digit is 9, and one of them is 0, we just have
to come up with three digits between 1 and 8,
inclusive, that total the remaining 11, since
0+9=9. 1+2+8=11, 1+3+7=11, 1+4+6=11, 2+3+6=11,
and 2+4+5=11.
We can't put the 0 first, so it's any arrangements
of the digits of these five 5-digit numbers that
don't have 0 first:
10289, 10379, 10469, 20369, 20459
For each of these 5 numbers,
There are 4 choices of positions to place the 0.
For each of those ways, there are 4 choices of positions to
place the smallest digit greater than 0.
For each of those ways, there are 3 choices of positions to
place the next digit in size.
For each of those ways, there are 2 choices of positions to
place the next to largest digit in size.
For each of those ways, there is only 1 choice of position to
place the largest digit in size, which is the 9.
So there are 5*4*4*3*2*1 = 480 possibilities.
Edwin
