MathDB
Six Classmates

Source: 2018 AMC 8 #11

November 20, 2018
probability2018 AMC 8AMC 8

Problem Statement

Abby, Bridget, and four of their classmates will be seated in two rows of three for a group picture, as shown. \begin{eqnarray*} \text{X}& \text{X} &\text{X} \\ \text{X}& \text{X} &\text{X} \end{eqnarray*} If the seating positions are assigned randomly, what is the probability that Abby and Bridget are adjacent to each other in the same row or the same column?
<spanclass=latexbold>(A)</span>13<spanclass=latexbold>(B)</span>25<spanclass=latexbold>(C)</span>715<spanclass=latexbold>(D)</span>12<spanclass=latexbold>(E)</span>23<span class='latex-bold'>(A) </span> \frac{1}{3} \qquad <span class='latex-bold'>(B) </span> \frac{2}{5} \qquad <span class='latex-bold'>(C) </span> \frac{7}{15} \qquad <span class='latex-bold'>(D) </span> \frac{1}{2} \qquad <span class='latex-bold'>(E) </span> \frac{2}{3}