I'm trying to figure out the following: A bowl contains balls with eight different colors, one of which is red. Assuming there are at least $20$ balls of each color, how many ways can a total of $20$ balls be distributed among the eight different colors if
(1) the bowl must contain at least four red balls?
(2) must contain at most $3$ red balls?
For (1), I got $245,157$. Is this correct? $(16 + 8 - 1)C16$
Also, any clues or hints to solve the second part would be appreciated!