<p>The letters A, B, C, D, and E are to be arranged in five different boxes, one in each box in the following way. A must be between C and D, B must be next to E, and C cannot be in the first or fifth positions. How many different arrangements of these letters are possible?</p>
<p>How can you compute that it's 4?</p>
<p>Ok, i think i remember this one from the SAT i took in January and got an 800 in math.</p>
<p>Just go through this problem slowly.</p>
<p>Since A has to be between two letters A cannot be the first or last letter.
Also, the CAD or DAC has to be part of the arrangement. (because A is between C and D). </p>
<p>Since C cannot be in the first or fifth position CAD can either be</p>
<p><em>CAD</em> or _ _ CAD</p>
<p>But since B has to be next to E, the second choice is the one that works.</p>
<p>Now, the second choice can either be
BECAD
EBCAD</p>
<p>And since we said earlier that it can be CAD or DAC, the remaining scenarios are
BEDAC
EBDAC</p>
<p>But C can’t be in the fifth spot.</p>
<p>So shouldn’t it be:</p>
<p>DACBE, BECAD, EBCAD, DACEB</p>
<p>Anyway, is there an algebraic method because I’m worried that when I take the SAT it’s going to be more numbers and I can’t just list them all out…</p>
<p>Yep you got it right, sorry about my error. </p>
<p>For this one, I think you just have to list them out. Go through it as I did (except do it correctly 
)</p>
<p>I just listed them out and got…</p>
<p>BECAD
EBCAD
DACEB
DACBE </p>
<p>Are those the 4?
No idea how to do it algebraically…!</p>
<p>on this one you can only list them</p>