MathDB
License plates.

Source: AMC 10 2006A, Problem 18

February 6, 2006
AMC

Problem Statement

A license plate in a certain state consists of 4 digits, not necessarily distinct, and 2 letters, also not necessarily distinct. These six characters may appear in any order, except that the two letters must appear next to each other. How many distinct license plates are possible? <spanclass=latexbold>(A)</span>104262<spanclass=latexbold>(B)</span>103263<spanclass=latexbold>(C)</span>5104262<spanclass=latexbold>(D)</span>102264<spanclass=latexbold>(E)</span>5103263 <span class='latex-bold'>(A) </span> 10^4\cdot 26^2 \qquad <span class='latex-bold'>(B) </span> 10^3\cdot 26^3 \qquad <span class='latex-bold'>(C) </span> 5\cdot 10^4\cdot 26^2 \qquad <span class='latex-bold'>(D) </span> 10^2\cdot 26^4\\ <span class='latex-bold'>(E) </span> 5\cdot 10^3\cdot 26^3