document.write( "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? \n" ); document.write( "
Algebra.Com's Answer #797078 by math_helper(2461)\"\" \"About 
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Let's choose P, VP, then S... this is the most straightforward way to go:

\n" ); document.write( "(20C1)(30C1)(48C1) = 20*30*48 = \"+highlight%2828800%29+\"
\n" ); document.write( "The 48 comes from the total 50 - 1 (female for P) - 1 (male for VP) = 48
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\n" ); document.write( "\n" ); document.write( "But, you say, what if you choose S first?
\n" ); document.write( "Ok, let's do that case.
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\n" ); document.write( "\n" ); document.write( "Choose S first, then P, then VP:\r
\n" ); document.write( "\n" ); document.write( "Two independent ways to choose S: (i) female, (ii) male
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\n" ); document.write( "\n" ); document.write( "(i) female S: (20C1)(19C1)(30C1) = 20*19*30 = 11400

\n" ); document.write( "PLUS

\n" ); document.write( "(ii) male S: (30C1)(20C1)(29C1) = 30*20*29 = 17400

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\n" ); document.write( "The total # of ways is 11400+17400 = 28800, just as we obtained before.\r
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