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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 isor 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.
