permutation with limited repetition

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 github.com/ctrimble/combinatorics –  C. Trimble Jan 7 at 0:23