<PRE><B>Question 1172162</B>
Let&#39;s choose P, VP, then S... this is the most straightforward way to go:&lt;br&gt;
(20C1)(30C1)(48C1) = 20*30*48 = {{{ highlight(28800) }}}
The 48 comes from the total 50 - 1 (female for P) - 1 (male for VP) = 48
&lt;br&gt;

But, you say, what if you choose S first?  
Ok, let&#39;s do that case.&lt;br&gt;

Choose S first, then P, then VP:

Two independent ways to choose S: (i) female, (ii) male&lt;br&gt;

(i) female S:  (20C1)(19C1)(30C1) = 20*19*30 = 11400&lt;br&gt;
PLUS&lt;br&gt;
(ii) male S:   (30C1)(20C1)(29C1) = 30*20*29 = 17400&lt;br&gt;
                                              
The total # of ways is 11400+17400 = 28800, just as we obtained before.




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