<p>In the Section 6 (Math) of the 4th practice in the latest edition of the Blue Book, the final question reads:</p>
<p>[a] ** [c] [d] <a href="these%20are%20cards...">e</a></p>
<p>If the five cards shown above are placed in a row so that [c] is never at either end, how many different arrangements are possible? </p>
<p>I haven't done counting problems for four years, so I'm a little...erm...rusty with this one. The correct answer is 72, could someone kindly work it out for me? Thanks!</p>
<p>Wait, I actually figured out. In case anyone looking at this thread is wondering the same thing:</p>
<p>Start with the first slot: there are 4 possible options, since [c] cannot be here</p>
<p>Move onto the final slot: there are 3 possible options, as [c] also cannot be here, and one card that could’ve occupied this slot was used in the first slot</p>
<p>Move onto the second slot: there are 3 possible options, as [c] can be used here, but two cards that could’ve occupied this slot are used in the two outside slots</p>
<p>Move onto the third slot: there are 2 possible options, as [c] can also be used here, but now three cards that could’ve occupied this slot are in other slots</p>
<p>Finally, move onto the fourth slot: there is 1 possible option, as [c] can be used here, but 4 cards that could’ve occupied that slot fill up all of the other slots.</p>
<p>Multiple those values all together and kaBAM, you have your answer: 72.</p>