document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192079>Question 1192079</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A math club has 30 members. During their acquaintance gathering, they have to choose 3 officers: president, vice  -  president, and secretary. If each office is to be held by 1 person and no person can hold more than one office, how many ways can these offices be filled? </SPAN>\n" );
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document.write( "Start at 30 and count down by 1 until three slots are filled.\r<BR>\n" );
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document.write( "30 choices for president<BR>\n" );
document.write( "29 choices for VP<BR>\n" );
document.write( "28 choices for secretary\r<BR>\n" );
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document.write( "Then multiply out those items.<BR>\n" );
document.write( "There are 30*29*28 = <font color=red>24,360</font> different ways to fill these three positions. Order matters.\r<BR>\n" );
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document.write( "Order matters because ABC is different from BAC as shown below<ul><li>ABC means person A is president, B is VP, C is secretary</li><li>BAC means person B is president, A is VP, C is secretary</li></ul>This is just one example.\r<BR>\n" );
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document.write( "Since order matters, you can use the nPr permutation formula with n = 30 and r = 3. This is an alternative pathway but the steps mentioned above are an easier route.<BR>\n" );
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