document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=984391>Question 984391</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The legislature of Puerto Rico consists of a 27-member Senate and a 51-member House of Representatives.\r<BR>\n" );
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document.write( "How many ways are there to choose a group of six members from the Puerto Rican legislature?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #605194 by </B><A HREF=/tutors/aboutme.mpl?userid=mathmate><B>mathmate(429)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathmate><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=mathmate><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=605194\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">   <BR>\n" );
document.write( "Given:<BR>\n" );
document.write( "There are 27+51=78 members of the legislature.<BR>\n" );
document.write( "Find the number of ways to choose a 6-member group from the legislature.<BR>\n" );
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document.write( "Solution:<BR>\n" );
document.write( "There are 78 choices to choose the first member,<BR>\n" );
document.write( "77 choices to choose the second, ...<BR>\n" );
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document.write( "73 choices to choose the sixth member<BR>\n" );
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document.write( "So there is a total of<BR>\n" );
document.write( "78*77*76*75*74*73=184933148400 ways to choose.<BR>\n" );
document.write( "However, there are 6! ways to arrange among the six members, so the total number of ways to choose 6 members <BR>\n" );
document.write( "=184933148400/6!=256851595 ways.<BR>\n" );
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document.write( "This can also be solved by the combination function,<BR>\n" );
document.write( "C(78,6)=78!/((78-6)!6!)<BR>\n" );
document.write( "=256851595 ways<BR>\n" );
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