The monotonic number is made of digits 1, 2, …, 9, such that each subsequent number equal to or greater than the previous number. Examples: 11119, 12369, 18999 etc.

I understand that I can isolate the first and last digit, leaving me with 3 numbers, e.g. 117, 223, 789 etc. 

The 1st digit can be 1-9, there are 9 cases. And the 2nd digit varies depending on the 1st one, and so does the 3rd digit.

My visualisation:

Case '1' = 9 cases for middle digit -> branches out to 9 cases for third digit

Case '2' = 8 cases for middle digit -> branches out to 8 cases for third digit
...
...

This is where I'm stuck...

Edit: actually the five-digit numbers don't have to start with 1 and end with 9. My bad. I don't even seem to be comprehending my own homework question properly.