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Turkey NMO 2000 1st Round - P11 (Combinatorics)

Source:

July 24, 2012

Problem Statement

In how many ways can 77 red, 77 white balls be distributed into 77 boxes such that every box contains exactly 22 balls?
<spanclass=′latex−bold′>(A)</span> 163<spanclass=′latex−bold′>(B)</span> 393<spanclass=′latex−bold′>(C)</span> 858<spanclass=′latex−bold′>(D)</span> 1716<spanclass=′latex−bold′>(E)</span> None <span class='latex-bold'>(A)</span>\ 163 \qquad<span class='latex-bold'>(B)</span>\ 393 \qquad<span class='latex-bold'>(C)</span>\ 858 \qquad<span class='latex-bold'>(D)</span>\ 1716 \qquad<span class='latex-bold'>(E)</span>\ \text{None}
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