Question 3491
 You did not mention that how many total digits in the decreasing number.

 In fact,the longest possible decreasing integer is 9876543210. iT
 contains 10 digits.
 Now, I consider all possible cases:
 
 (i)Ten digits: C(10,10) = 1. [There is only one number,namely 9876543210]
 (ii)Nine digits: there are C(10,9) = 10 dec. numbers.
 ...
 r digits, r>=2,: there are C(10,r) dec. numbers.

 Totally, there are C(10,10)+C(10,9)+..+C(10,2) = 2^10 -C(10,1) -C(10,0)
 = 1024 - 11 = 1013 such dec. numbers. (two or more digits)

 Kenny