3-letter combination Please forgive me for this amateur question in advance.
I have 3 letters, A, B & C. I want to find out how many combinations can I make from 1 to 10 characters using these 3 letters.
Say: AAAAAAAAAA, AAAAAAAAAB, AAAAAAAAAC etc.
Where AAAAAAAAAC = AAAACAAAAA = ACAAAAAAAA. (This set is equally the same because of the occurence of a single C)
or say AAAB = ABAA = BAAA.
or say BBBC = BCBB = CBBB.
from 1 to 10 characters.
I hope this is clear. Please help.

Hint :
Rephrasing, given four symbols $\{A,B,C,0\}$ how many $10-$lettered combinations possible? $0$ symbol for blank spaces.
Let each symbol occur $a_{i}$ times ($i=1,2,3,4$) and $a_{i}\in{0,1,\ldots10} $. Then solution for $$ a_{1} + a_{2} + a_{3} + a_{4} = 10 $$ is given by $^{10+4-1}C_{4-1}=286$ using stars and bars. Subtracting $1$ from it, to not account for the case when all $0$s used, 285 is final answer.
