A hint to get started
Separate repeated-ball selections into disjoint cases
A box contains 8 balls, of which 3 are identical (and so are indistinguishable from one another) and the other 5 are different from each other. 3 balls are to be picked out of the box, the order in which they are picked out does not matter. Find the number of different possible selections of 3 balls.
[2006/I/4]
CJC · Discussion · Question 9
Count visible selections, not the physical identities of identical balls.