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P16 [Combinatorics] - Turkish NMO 1st Round - 2013

Source:

April 20, 2013
probability

Problem Statement

1616 white and 44 red balls that are not identical are distributed randomly into 44 boxes which contain at most 55 balls. What is the probability that each box contains exactly 11 red ball?
<spanclass=′latex−bold′>(A)</span> 564<spanclass=′latex−bold′>(B)</span> 18<spanclass=′latex−bold′>(C)</span> 44(164)<spanclass=′latex−bold′>(D)</span> 54(204)<spanclass=′latex−bold′>(E)</span> 332 <span class='latex-bold'>(A)</span>\ \dfrac{5}{64} \qquad<span class='latex-bold'>(B)</span>\ \dfrac{1}{8} \qquad<span class='latex-bold'>(C)</span>\ \dfrac{4^4}{\binom{16}{4}} \qquad<span class='latex-bold'>(D)</span>\ \dfrac{5^4}{\binom{20}{4}} \qquad<span class='latex-bold'>(E)</span>\ \dfrac{3}{32}
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