Counting

How many positive integers are there whose digits strictly decrease from left to right,     

and have at most one even digit, and the sum of the digits is 6?    

 6 0          This is legit, because zero isn't even.  Somebody might argue definitions.    

 5 1    

 5 1 0    

 4 2           Won't work, problem says there can't be more than one even digit.    

 3 2 1    

 3 2 1 0    

By the terms of the problem, I find 5 of them.    

_.