MathDB
AMC 8 2008 Problem 14

Source:

November 28, 2010

Problem Statement

Three A’s\text{A's}, three B’s\text{B's}, and three C’s\text{C's} are placed in the nine spaces so that each row and column contain one of each letter. If A\text{A} is placed in the upper left corner, how many arrangements are possible? [asy] size((80)); draw((0,0)--(9,0)--(9,9)--(0,9)--(0,0)); draw((3,0)--(3,9)); draw((6,0)--(6,9)); draw((0,3)--(9,3)); draw((0,6)--(9,6)); label("A", (1.5,7.5)); [/asy] <spanclass=latexbold>(A)</span> 2<spanclass=latexbold>(B)</span> 3<spanclass=latexbold>(C)</span> 4<spanclass=latexbold>(D)</span> 5<spanclass=latexbold>(E)</span> 6 <span class='latex-bold'>(A)</span>\ 2\qquad<span class='latex-bold'>(B)</span>\ 3\qquad<span class='latex-bold'>(C)</span>\ 4\qquad<span class='latex-bold'>(D)</span>\ 5\qquad<span class='latex-bold'>(E)</span>\ 6