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Flag-Colored Beads

Source: AMC 10 2008B Problem 22

March 1, 2008
probabilitycountingdistinguishabilityAMC

Problem Statement

Three red beads, two white beads, and one blue bead are placed in a line in random order. What is the probability that no two neighboring beads are the same color? <spanclass=′latex−bold′>(A)</span> 112<spanclass=′latex−bold′>(B)</span> 110<spanclass=′latex−bold′>(C)</span> 16<spanclass=′latex−bold′>(D)</span> 13<spanclass=′latex−bold′>(E)</span> 12 <span class='latex-bold'>(A)</span>\ \frac{1}{12} \qquad <span class='latex-bold'>(B)</span>\ \frac{1}{10} \qquad <span class='latex-bold'>(C)</span>\ \frac{1}{6} \qquad <span class='latex-bold'>(D)</span>\ \frac{1}{3} \qquad <span class='latex-bold'>(E)</span>\ \frac{1}{2}
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