MathDB
1994 AMC 12 #22

Source:

December 30, 2011
AMC

Problem Statement

Nine chairs in a row are to be occupied by six students and Professors Alpha, Beta and Gamma. These three professors arrive before the six students and decide to choose their chairs so that each professor will be between two students. In how many ways can Professors Alpha, Beta and Gamma choose their chairs?
<spanclass=latexbold>(A)</span> 12<spanclass=latexbold>(B)</span> 36<spanclass=latexbold>(C)</span> 60<spanclass=latexbold>(D)</span> 84<spanclass=latexbold>(E)</span> 630 <span class='latex-bold'>(A)</span>\ 12 \qquad<span class='latex-bold'>(B)</span>\ 36 \qquad<span class='latex-bold'>(C)</span>\ 60 \qquad<span class='latex-bold'>(D)</span>\ 84 \qquad<span class='latex-bold'>(E)</span>\ 630