<PRE><B>Question 541690</B>
&lt;br&gt;&lt;font face=&quot;Tahoma&quot;&gt;This is one of those counting method problems, using the multiplication principle.&lt;br&gt;
In this case, we have very specific rules for selecting the representatives.&lt;br&gt;
There are 3 positions, how many ways can we &quot;choose&quot; each position?&lt;br&gt;
In the first slot, we can only place a woman, so we have 2 choices.&lt;br&gt;
In the second slot, we can only place a man so we have 3 choices.&lt;br&gt;
In the third slot, we can only place a man (who wasn&#39;t already chosen), so we have ONLY 2 choices.&lt;br&gt;
This because we assume one person can&#39;t be both the secretary and the treasurer at the same time.&lt;br&gt;
Then we just need to multiply the number of choices!&lt;br&gt;
In this case we have&lt;br&gt;
{{{2*3*2}}}&lt;br&gt;
which equals {{{12}}}&lt;br&gt;
I hope this helps!&lt;br&gt;</PRE>