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P11 [Combinatorics] - Turkish NMO 1st Round - 2003

Source:

May 14, 2014
probability

Problem Statement

What is the probability of having no BB before the first AA in a random permutation of the word ABRAKADABRA\text{ABRAKADABRA}?
<spanclass=′latex−bold′>(A)</span> 23<spanclass=′latex−bold′>(B)</span> 57<spanclass=′latex−bold′>(C)</span> 56<spanclass=′latex−bold′>(D)</span> 67<spanclass=′latex−bold′>(E)</span> None of the preceding <span class='latex-bold'>(A)</span>\ \dfrac 23 \qquad<span class='latex-bold'>(B)</span>\ \dfrac 57 \qquad<span class='latex-bold'>(C)</span>\ \dfrac 56 \qquad<span class='latex-bold'>(D)</span>\ \dfrac 67 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}
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