<p>From an old previous thread:</p>
<p>"3 men and 3 women stand in 1 line. Two or more of the same gender cannot stand next to each other. How many different arrangements are possible?"</p>
<p>Isn't the answer just 2?
MWMWMW
WMWMWM</p>
<p>Thanks for your help!</p>
<p>Each M is different - Joe, Harold, Stewart and each W is different Laura, Sue, Jessa. Now try it again.</p>
<p>So isn’t this now the Counting Principle? So if the question were to be phrased as:</p>
<p>“Joe, Harold, Stewart and Laura, Sue, and Jessa stand in a line. Two or more of the same gender cannot stand next to each other. How many different arrangements are possible?”</p>
<p>3^3 = 27 --> 27 arrangements BUT the same gender can’t stand next to each other so 27/3 = 9 Arrangements?</p>
<p>To be honest at this point I’m guessing 9 without taking the time to list them all. </p>
<p>It IS the counting principle. You have six slots to fill. Let’s go through each spot and ask that key question: “Now, how many choices do we have?”</p>
<p>First spot: 6 choices – you can pick anyone you want
Second spot: 3 choices – any one of the opposite gender as spot 1
Third spot: 2 choices – the remaining two of the same gender as spot #1
4th spot: 2 choices – the remaining two of the same gender as spot #2
5th spot: 1 choice – the last remaining person of the same gender as spot #1
6th spot: 1 choice – the last remaining person of the same gender as spot #2</p>
<p>Now just multiply…</p>