MathDB
Professor Chang

Source: 2018 AMC 8 #16

November 20, 2018
AMC 82018 AMC 8

Problem Statement

Professor Chang has nine different language books lined up on a bookshelf: two Arabic, three German, and four Spanish. How many ways are there to arrange the nine books on the shelf keeping the Arabic books together and keeping the Spanish books together?
<spanclass=latexbold>(A)</span>1440<spanclass=latexbold>(B)</span>2880<spanclass=latexbold>(C)</span>5760<spanclass=latexbold>(D)</span>182,440<spanclass=latexbold>(E)</span>362,880<span class='latex-bold'>(A) </span>1440\qquad<span class='latex-bold'>(B) </span>2880\qquad<span class='latex-bold'>(C) </span>5760\qquad<span class='latex-bold'>(D) </span>182,440\qquad <span class='latex-bold'>(E) </span>362,880