<p>I hope you enjoyed the Wizard of Oz reference. </p>
<p>Anyways, I just cannot seem to get these problems down! Here is one I am having trouble with below, please walk me through this and show me how you approach these types of problems:</p>
<p>A club has 14 members, consisting of 6 men and 8 women. How many slates of 3 officers - president, vice president, and secretary - can be formed if the president must be a woman and the vice president must be a man?</p>
<p>I have the answer, but am in desperate need of help and guidance. Thanks!</p>
<p>What is the answer, I’m not the greatest at combinations. I think I know how to do it, but I don’t want to give wrong directions if I am just making things up.</p>
<p>The answer is: 576</p>
<p>Think of how you find combinations.</p>
<p>You have 3 ‘spots’ that need filled. Normally, if there weren’t special circumstances, it would just be 14<em>13</em>12=1872</p>
<p>But, there are special circumstances. Before going back to the ‘normal’ method, you must handle these circumstances.</p>
<p>President must be a woman. There are 8 women, so possibilities for this spot is 8.</p>
<p>Vice President must be male. There are 6 men, so there are 6 possibilities for this spot.</p>
<p>Now you have the ‘anybody’ spot of secretary. You already have 1 male saved for VP and 1 woman save for P, so their are 12 possibilities for this spot.</p>
<p>Now just multiply 12<em>6</em>8</p>
<p>There are 3 positions, which I’ll shorten to p, v, & s</p>
<p>p must be a woman; therefore, there are 8 choices.
v must be a man; therefore, there are 6 choices.
s can be of either gender. However, neither p nor v can be s since one person can’t have two positions. Therefore, there are 12 choices.</p>
<p>8<em>6</em>12 = 576</p>