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Nebraskan License Plates

Source:

January 9, 2009

Problem Statement

Nebraska, the home of the AMC, changed its license plate scheme. Each old license plate consisted of a letter followed by four digits. Each new license plate consists of three letters followed by three digits. By how many times is the number of possible license plates increased? <spanclass=′latex−bold′>(A)</span> 2610<spanclass=′latex−bold′>(B)</span> 262102<spanclass=′latex−bold′>(C)</span> 26210<spanclass=′latex−bold′>(D)</span> 263103<spanclass=′latex−bold′>(E)</span> 263102 <span class='latex-bold'>(A)</span>\ \frac{26}{10} \qquad <span class='latex-bold'>(B)</span>\ \frac{26^2}{10^2} \qquad <span class='latex-bold'>(C)</span>\ \frac{26^2}{10} \qquad <span class='latex-bold'>(D)</span>\ \frac{26^3}{10^3} \qquad <span class='latex-bold'>(E)</span>\ \frac{26^3}{10^2}
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