Question 981031
How many 3- digit numbers have the units larger than the tens digit?
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It's easier if we interpret that problem as if it had read:
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How many 3- digit numbers have the tens smaller than the units digit?
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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</pre>