How many DECREASING NUMBERS are there?

I remember doing a lot of Math problems over the years, but not one that could span many class years.  Hear is one, that if teachers all took some time, could be used from 2nd grade on.  As you can see the question asks how many decreasing numbers are there?  First, what is a decreasing number?  Second, where do I start?  Third, why undertake a project of this magnitude?
1. A decreasing number is any number where all digits contained in the number are less than the previous digit.  With that as a definition, the numbers 22, 326, and 567 are not decreasing.  The 2 and 2 are of course equal, although 2 is less than 3, the 6 is greater than the 2, and in 567 the digits are increasing.  We have two new important terms of Math in our bank.
These numbers are in the family of decreasing numbers, 74, 310, 54321.  As we see in each example, the digits decrease from left to right.
2.  George Polya, the great American Mathematician of the early 20th Century always said, "When a problem is to big to solve, start small, and build up through a pattern".  This is what I propose you do.  In the 2nd grade we figure out how many decreasing numbers there are below 100.  That is, we start small, and we begin to build successes on a difficult problem.  So, what is the first decreasing number?  It is 10 of course.  But the next one is 20, and 21 then 30, 31, and 32.  The last decreasing 2–digit number is 98.
Your 2nd grade class's job is to figure out exactly how many there are.
3. I know many of you are wondering why do it.  For two reasons, why not, and to discover a true beauty in numbers.  There is not a infinite number of decreasing numbers.  After all, we only have 10 digits, thus we have a largest decreasing number 9,876,543,210.  Also, there is only one of this size.
So, as your students move from 2nd to 3rd grade we simply ask for the number of decreasing numbers to a higher number, lets say 500.  Like our 2–digit numbers, with our 3–digit numbers we need to develop a pattern, and that is the power we are placing in the hands of our youngsters.  The first decreasing 3–digit number is 210, and the next is 310.  We need not gasp at the amount of them, because there are not that many of them.  However, as we develop the pattern it starts to become fun.
Enjoy the process of this problem, and let them enjoy the creation of the pattern.