<p>Can someone help me with a SAT math question? It's in the giant blue book, test #2, Question #18, page 476. It involves five different types of squares.</p>
<p>If the 5 cards show above are placed in a row so that <a href="one%20particular%20box"></a> is never at either end, how many different arrangements are possible?</p>
<p>thanks you guys! and good luck tmr!</p>
<p>My reasoning- the particular box that can't go on either side only has 3 options to be placed- the middle 3 slots. The next box can go anywhere, but there's already a slot occupied by the 1st box. So, box 2 has 4 options. Box 3 has 3 options, Box 4 has 2, then the last box has to go in the last remaining slot. Hence, 3 times 4 times 3 times 2 times 1=72. I think that's right</p>
<p>Good luck to you too~~</p>
<p>correct! thank you!</p>
<p>or u can use a method of permutations
there are a total of 120 ways the boxes can be arranged (5 factorial)
then if u have a dark square on one side- there are 24 ways the other boxes can be arranged (4 factorial)
then if u have the dark square on the other side- there are 24 ways the other boxes can be arranged (4 factorial)</p>
<p>multiply 24 by 2
then do total number of possibilities minus possibilities with dark square on either side ( 48 - 24 when box is one side and 24 when box is on the other)</p>
<p>120-48 = 72
or u can do it his way above :)</p>
<p>SATs suck a lot - i love your username. they honestly do suck a lot. gotta take them for the first time in March! :-P</p>
<p>Question: for this question, is it possible to solve it by multiplying together the possibilities for each of the spots instead of the possibilities for each of the cards? If so how would you do that?</p>
<p>Thanksss!</p>