Suppose there are 8 boxes and many balls of 7 different colours. We have to fill all the boxes with balls with the restriction that balls of a particular colour can not be placed in more than 2 boxes. It may be possible that ball of a particular colour is not selected at all. There is a sufficient supply of ball of each colour. What is the total number of ways this can be done?
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As I understand your question the answer is 0. you say there are more boxes than colours of balls, you say that all boxes must be filled with balls, and say that a colour cannot be on more than one box. This is impossible.
But I am guessing I mis-interpreted your question