§ take at most 4 letters from 15 letters.
Trivial: use .
Combinatorially, we know that .
We can apply the same here, to get .
But what does this mean, combinatorially? We are adding a dummy letter, say ,
which if chosen is ignored. This lets us model taking at most 4 letters by adding
4 dummy letters and then ignoring these if we pick them up; we
pick 4 letters from 15 + 4 dummy = 19 letters.
I find it nice how I used to never look for the combinatorial meaning behind
massaging the algebra, but I do now.