document.write( "Question 1022266: Please help me with this problem!
\n" ); document.write( "A club has 43 members, 19 are age greater than or equal
\n" ); document.write( "to 30 years old and 24 are age less than 30 years old.
\n" ); document.write( "A slate of 6 officers will be elected including a
\n" ); document.write( "president, vice president, treasury, Sargent of arms
\n" ); document.write( "and press liaison.\r
\n" ); document.write( "\n" ); document.write( "How many slates of 6 officers are there in which the
\n" ); document.write( "president and vice president are not from the same age
\n" ); document.write( "group. (Helpful hint: One is age greater than equal to
\n" ); document.write( "30 years old and one is less than 30 years old) \n" ); document.write( "

Algebra.Com's Answer #638256 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!
Please help me with this problem!
\n" ); document.write( "A club has 43 members, 19 are age greater than or equal
\n" ); document.write( "to 30 years old and 24 are age less than 30 years old.
\n" ); document.write( "A slate of 6 officers will be elected including a
\n" ); document.write( "president, vice president, secretary, treasurer,
\n" ); document.write( "sergeant-at-arms and press liaison.
\n" ); document.write( "

\r\n" );
document.write( "How many slates of 6 officers are there in which the \r\n" );
document.write( "president and vice president are not from the same age \r\n" );
document.write( "group. (Helpful hint: One is age greater than equal to \r\n" );
document.write( "30 years old and one is less than 30 years old).\r\n" );
document.write( "\r\n" );
document.write( "First we find the number of ways to choose the top \r\n" );
document.write( "pair of officers:\r\n" );
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document.write( "Case 1: The president is 30 or older and the \r\n" );
document.write( "vice-president is younger than 30.\r\n" );
document.write( "19 ways to choose the president\r\n" );
document.write( "24 ways to choose the vice-president\r\n" );
document.write( "\r\n" );
document.write( "That's 19*24 = 456 ways to have the president older \r\n" );
document.write( "and the vice-president younger\r\n" );
document.write( "\r\n" );
document.write( "Case 2:  The president is younger than 30 and the \r\n" );
document.write( "vice-president is 30 or older. \r\n" );
document.write( "24 ways to choose the president\r\n" );
document.write( "19 ways to choose the vice-president\r\n" );
document.write( "\r\n" );
document.write( "That's also 24*19 = 456 ways to have the president \r\n" );
document.write( "younger and the vice-president older.\r\n" );
document.write( "\r\n" );
document.write( "So there are 2*456 or 912 ways to choose the pair \r\n" );
document.write( "of top officers.\r\n" );
document.write( "\r\n" );
document.write( "For each of these 912 choices for the pair of top \r\n" );
document.write( "officers, there remain:\r\n" );
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document.write( "41 ways to choose the secretary.\r\n" );
document.write( "40 ways to choose the treasurer.\r\n" );
document.write( "39 ways to choose the sergeant-at-arms.\r\n" );
document.write( "38 ways to choose the press liason.\r\n" );
document.write( "\r\n" );
document.write( "That's 912*41*40*39*38 = 2216597760 ways.\r\n" );
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document.write( "Edwin

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