Suppose there are three types of balls: red R balls, blue B balls and green G balls. How many ways are there to distribute the bales in N different bins so that no bin is empty and that a bin can hold no more than one balloon of the same color?

Right here,

1) R, B, G <= N (no color should have more than N balls, because we have the condition that at most one ball of the same color is in a tray and that all balls must be placed )

and

2) R + B + G> = N (this is due to the fact that no basket is empty).