<ol>
<li>How many ways can seven books be arranged on a shelf if two of them are math books and must be kept together?</li>
</ol>
<p>Answer is 1440. Go figure.</p>
<p>First think of the 2 math books as one book. How many ways can the other 5 books (and the 6th book which is really 2 books) be arranged?</p>
<p>6! = 720</p>
<p>Now remember that one of those was actually two books, so in each arrangement you could reverse their order, doubling the number of arrangements.</p>
<p>2(6!) = 1440</p>
<p>Draw a small picture</p>
<hr>
<p>Since you know two must be kept together, you’ll get</p>
<p>x y _ _ _ _ _</p>
<p>5 additional spaces means 5! = 120, but move around the x and y and you’ll see there are 6 times more possibilities ( _ x y _ _ _ _ ) is one of these six possibilities. </p>
<p>So, 120 x 6 = 720</p>
<p>Since x and y can switch order, ( _ y x _ _ _ _ _ ), you have twice as many possibilities. </p>
<p>2 x 720 = 1440</p>
<p>This is a good trick to know. I’m bumping this and then I am gong to bump the puzzles I posted a couple of days ago…they are related. Besides…i’ve never bumped a thread before. So this is kind of a big moment for me. Here goes: BUMP</p>
<p>This technique with the line is amazing! I’m writing it down in my notebook</p>