document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1152786>Question 1152786</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A committee of 6 U.S. senators is to be formed with 3 Democrats and 3 Republicans. In how many ways can this be done if there are 61 Democratic senators and 39 Republican senators?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #774874 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52800)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=774874\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "Usually, such problems are solved in three lines:\r<BR>\n" );
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document.write( "    There are  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B61%5D%5E3 ALIGN=MIDDLE  ALT=\"C%5B61%5D%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2861%2A60%2A59%29%2F%281%2A2%2A3%29 ALIGN=MIDDLE  ALT=\"%2861%2A60%2A59%29%2F%281%2A2%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 35990 ways to select 3 democrats from 61 democrats.\r\n" );
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document.write( "    There are  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B39%5D%5E3 ALIGN=MIDDLE  ALT=\"C%5B39%5D%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2839%2A38%2A37%29%2F%281%2A2%2A3%29 ALIGN=MIDDLE  ALT=\"%2839%2A38%2A37%29%2F%281%2A2%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 9139 ways to select 3 republicans from 39 republicans.\r\n" );
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document.write( "    These selections are independent; therefore, the <U>final ANSWER</U> is the product of these numbers  35990*9139 = 328912610.\r\n" );
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document.write( "The symbols  &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5Bn%5D%5Ek ALIGN=MIDDLE  ALT=\"C%5Bn%5D%5Ek\"   DISABLED_style= \"max-width:90%; height:auto;\" >  &nbsp;denote &nbsp;<U>combinations</U> &nbsp;of &nbsp;\"n\" &nbsp;items taken &nbsp;\"k\"&nbsp; at a time.\r<BR>\n" );
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document.write( "On Combinations, &nbsp;see introductory lessons\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Permutations/Introduction-to-Combinations-.lesson>Introduction to Combinations</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Permutations/PROOF-of-the-formula-on-the-number-of-combinations.lesson>PROOF of the formula on the number of Combinations</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Permutations/Problems-on-Combinations.lesson>Problems on Combinations</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Permutations/OVERVIEW-the-lessons-on-Permutations-and-Combinations.lesson>OVERVIEW of lessons on Permutations and Combinations</A>\r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.\r<BR>\n" );
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document.write( "The referred lessons are the part of this online textbook under the topic &nbsp;\"<U>Combinatorics: Combinations and permutations</U>\". \r<BR>\n" );
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document.write( "Save the link to this textbook together with its description\r<BR>\n" );
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document.write( "Free of charge online textbook in ALGEBRA-II<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r<BR>\n" );
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document.write( "into your archive and use when it is needed.\r<BR>\n" );
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