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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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In the first sentence, maybe you should say there are 8 boxes and (a lot of) balls of 7 different colours. What you wrote means that you have only 7 balls, which are different colours. – user39280 Aug 19 '13 at 15:34
thanks... made some changes in my question – user1463308 Aug 19 '13 at 16:14
I assume two balls of the same color are not distinguishable? – Patrick Aug 19 '13 at 16:25
You are right. Two balls of the same color are not distinguishable. – user1463308 Aug 19 '13 at 16:29
I get 2,346,120 using the math utilities in – Christian Trimble Jan 7 '15 at 0:23

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

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I have mentioned that there is a sufficient supply of ball of each colour which means that ball of particular colour can be on more than one box. But as per the additional condition, it can not be on more than two boxes. – user1463308 Aug 19 '13 at 15:44

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