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Source: 2017 AMC 12A #14

February 8, 2017
AMCAMC 12AMC 12 A2017 AMC 12AAMC 10AMC 10 Acombinatorics

Problem Statement

Alice refuses to sit next to either Bob or Carla. Derek refuses to sit next to Eric. How many ways are there for the five of them to sit in a row of 55 chairs under these conditions?
<spanclass=latexbold>(A)</span> 12<spanclass=latexbold>(B)</span> 16<spanclass=latexbold>(C)</span> 28<spanclass=latexbold>(D)</span> 32<spanclass=latexbold>(E)</span> 40<span class='latex-bold'>(A)</span>\ 12\qquad<span class='latex-bold'>(B)</span>\ 16\qquad<span class='latex-bold'>(C)</span>\ 28\qquad<span class='latex-bold'>(D)</span>\ 32\qquad<span class='latex-bold'>(E)</span>\ 40