Hello, thefirsthokage!
There is no neat formula for this one.
I made a list . . . the shortest possible (I think).
We have these letters: .How many three-letter combos can be made from the word PROPORTION?
3 letters the same: . . . one way.
2 letters the same: there choices of the matching pair (
. . and choices for the third letter . . . ways.
3 differerent letters: there are ways.
Therefore, there are: three-letter combos.
Here is a second way the get the same answer as Soroban.
The coefficient of in the expansion of is 36.
However that is assuming that the word ‘combos’ means the same thing as multi-set. In the above reply <p,o,p> is a multi-set and is counted only once. If this word ‘combos’ means three letter strings the we would count pop, ppo and opp.
What is the intended meaning of ‘combos’?