Santa Claus has five toy airplanes of each of n plane models. How many ways are there to put one airplane in each of $r$ ($r \geq n$) identical stockings such that all models of planes are used?
Combinatorics counting, inclusion exclusion problem
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combinatorics
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4Trick Question: Santa Claus does not have a model in ZFC – 2011-11-11
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6Welcome to MathSE. I see that this is your first question. So I wanted to let you know a few things about MathSE. We like to know the sources of questions. We also like to know what you've tried on a problem or what your thoughts are, so that the answer does not re-invent the wheel or go over stuff you already know. These sort of pleasantries usually result in more and better answers. Thank you! – 2011-11-11
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2First, put one each of the $n$ plane models into stockings; that leaves $r-n$ stockings to be filled, with $4$ planes of each of $n$ types to be placed with no restrictions. – 2011-11-11
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1To show Im a complete egghead, I will correct my joke: ZFC$ \cup${Santa Claus} has no model. – 2011-11-11