How many n choose r include all n elements?

How many n choose r include all n elements?

Thank you for your comments -- hopefully a clarifying example --
In choosing all combinations of 4 elements from (A,B,C), (e.g.,
AAAA,BBBB,ACAB,BBBC, etc.) how many of these combinations include A, B and
C?
That is, where element order is considered and repetition allowed. I can't
seem to get my head around it. What I came up with was n choose r - (n
choose n-1) * (n-1 choose r) but the latter overlap and I was not sure how
to calculate the overlaps.
Can anyone please help?
Thanks in advance.