BB Test 2, Math Section 6, p476 #18: I have no idea how to do this problem

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<p>In the Blue Book, Practice Test #2, Math Section #6 on page 476...question 18...I have absolutely no idea how to solve this question.</p>

<p>There is a diagram of 5 different looking boxes. For purposes of posting this online, I'll call the boxes A, B, C, D, E.</p>

<p>The question is: If the 5 letters shown above are placed in a row so that C is never at either end, how many different arrangements are possible?</p>

<p>The answer is 72.</p>

<p>What is the quickest, easiest, most efficient way to do this? It's the last question in the section too, so the fastest method would be the most helpful.</p>

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<p>Arrangement problem, so the trick is largely in setting it up.</p>

<p>All right, so we know that C cannot be at either end. Therefore C can only take 1 of the 3 middle positions. This leaves 4 positions for another letter, then 3 positions for another letter, then 2 positions for another letter, and 1 position for the last letter.</p>

<p>3x4x3x2=72</p>

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<p>See <a href="http://talk.collegeconfidential.com/sat-preparation/339734-consolidated-list-blue-book-math-solutions-3rd-ed.html%5B/url%5D"&gt;http://talk.collegeconfidential.com/sat-preparation/339734-consolidated-list-blue-book-math-solutions-3rd-ed.html&lt;/a&gt;&lt;/p>