Question 1172162: In how many ways can a president, vice-president, and secretary be chosen from a class of 20 females and 30 males if the president must be a female and the vice president a male?
Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website! Let's choose P, VP, then S... this is the most straightforward way to go:
(20C1)(30C1)(48C1) = 20*30*48 = 
The 48 comes from the total 50 - 1 (female for P) - 1 (male for VP) = 48
But, you say, what if you choose S first?
Ok, let's do that case.
Choose S first, then P, then VP:
Two independent ways to choose S: (i) female, (ii) male
(i) female S: (20C1)(19C1)(30C1) = 20*19*30 = 11400
PLUS
(ii) male S: (30C1)(20C1)(29C1) = 30*20*29 = 17400
The total # of ways is 11400+17400 = 28800, just as we obtained before.
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