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P04 [Combinatorics] - Turkish NMO 1st Round - 2014

Source:

May 21, 2014
probability

Problem Statement

What is the probability of having 22 adjacent white balls or 22 adjacent blue balls in a random arrangement of 33 red, 22 white and 22 blue balls?
<spanclass=′latex−bold′>(A)</span> 25<spanclass=′latex−bold′>(B)</span> 37<spanclass=′latex−bold′>(C)</span> 1635<spanclass=′latex−bold′>(D)</span> 1021<spanclass=′latex−bold′>(E)</span> 514 <span class='latex-bold'>(A)</span>\ \dfrac{2}{5} \qquad<span class='latex-bold'>(B)</span>\ \dfrac{3}{7} \qquad<span class='latex-bold'>(C)</span>\ \dfrac{16}{35} \qquad<span class='latex-bold'>(D)</span>\ \dfrac{10}{21} \qquad<span class='latex-bold'>(E)</span>\ \dfrac{5}{14}
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