I think the problem here is 11 P 6 is not counting what you think it is. Rather, it's counting the number of ways to pick 6 of the 11 boxes, where the order picked matters. Like this, where 1,2,3,4,5,6 means the order it was chosen and - means it was not chosen:
{1,2,3,4,5,6,-,-,-,-,-}...