They are all "hard" to find, even "standard" 5 door manual in black because that is a choice between 3 doors and 5 (about 25% will be three door), manual vs DSG (about 30% will be manual) and black is certainly not the most popular colour out of ~10 different colour choices - probably 10%. Then there is the possibility of dozens of different extras which you don't want. Probably 90% of the cars out there have some other extra added.
Nothing "easy" about your spec... and then it needs to be in the part of the Uk that you are prepared to travel too...
I'd do the mathematical probability but my brain hurts too much!
Definitely slim chances though.