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P08 [Combinatorics] - Turkish NMO 1st Round - 2014

Source:

May 21, 2014

Problem Statement

In how many ways can 1717 identical red and 1010 identical white balls be distributed into 44 distinct boxes such that the number of red balls is greater than the number of white balls in each box?
<spanclass=latexbold>(A)</span> 5462<spanclass=latexbold>(B)</span> 5586<spanclass=latexbold>(C)</span> 5664<spanclass=latexbold>(D)</span> 5720<spanclass=latexbold>(E)</span> 5848 <span class='latex-bold'>(A)</span>\ 5462 \qquad<span class='latex-bold'>(B)</span>\ 5586 \qquad<span class='latex-bold'>(C)</span>\ 5664 \qquad<span class='latex-bold'>(D)</span>\ 5720 \qquad<span class='latex-bold'>(E)</span>\ 5848