Well there is a handy formula: The number of ways of choosing k things from n with replacement is: See Wikipedia. Note that because it is with replacement there is nothing wrong with . Either can be any non-negative number.
Now if you ask the question, how many ways are there to distribute n objects to k bins (people, etc.) you can think of the problem on its head. Each of n objects are going to pick a bin (people, etc.). Since 2 different objects could pick the same bin, this is picking n from k with replacement. So this is or equivalently
So going back to your question: You are going to distribute 4 Dalis to 5 people: . You are going to distribute 5 VG's to 5 people: . And of course:
Since you can think of each collection by the same painter independently you just multiply them.