How many 3- digit numbers have the units larger than the tens digit?
It's easier if we interpret that problem as if it had read:
How many 3- digit numbers have the tens smaller than the units digit?
There is/are:
1 digit smaller than 1,
2 digits smaller than 2,
...
9 digits smaller than 9.
That's 1+2+3+4+5+6+7+8+9 = 45 ways to choose the tens and units digits.
For each of those there are 9 ways to choose the hundreds digit.
Total: 45*9 = 405
Edwin
