Combination Math Problem: Choosing 5 Balls from 4 Boxes without Restriction

[Harmony]

Question Statement
4 boxes each contain a large number of identical balls, those in 1 box are red, those in the 2nd box are blue, those in the 3rd box are yellow and those in the remaining box are green. In how many ways can a set of five balls be chosen? (without restriction)

My thoughts
If the question is asking for the permutation, then the answer is 4^5 (since there is 4 colour and the colour can be repeated)

But the question is asking for combinations. How should I attempt this question? Should I consider cases where all colours are the same/ different, 2 same 3 different...etc.?

 

[f(x)]

But the question is asking for combinations. How should I attempt this question? Should I consider cases where all colours are the same/ different, 2 same 3 different...etc.?

yes...you can have all of same color , or two of same color and 3 of 3 different colors ans so on