Edit: I have completely reworded this question to be more math-friendly.
How many ways can a 'word*' be 'divvied*' up into 'boxes*'?
A box is a letter container that may contain up to N letters of a word. The order of the letters in the box matters.
Divvying of a word means "to spread out, or disburse, the words' letters between box(es), in such a way that setting non-empty boxes adjacent to one another creates a correct spelling of the original word.
A word is a string of 'X' letters in which the order of the letters matters.
I might have a further question about re-understanding this with "uniqueness" in mind, but I don't actually need to know that right now I do not think.
Example Word - Telecommunication
Divvied Up One Configuration
One More Configuration