You have infinitely many balls and each of them is colored with one of the $C$ colors. You decided to fill each of the $N$ boxes $(B_1, B_2, B_3, \ldots, B_N)$ with exactly one ball. In how many ways can you do that? Two ways are considered different if there is at least one box in one way that has different colored ball than in the other way.
I think the answer is $C^N$. Am I correct?
What would happen if the condition exactly one is removed?