document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1195580>Question 1195580</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A catering service offers 8 ​appetizers, 9 main​ courses, and 7 desserts. A banquet committee is to select 3 ​appetizers, 5 main​ courses, and 3 desserts. How many ways can this be​ done? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #828103 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</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=828103\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "A catering service offers 8 ​appetizers, 9 main​ courses, and 7 desserts. <BR>\n" );
document.write( "A banquet committee is to select 3 ​appetizers, 5 main​ courses, and 3 desserts. <BR>\n" );
document.write( "How many ways can this be​ done?<BR>\n" );
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document.write( "There are  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B8%5D%5E3 ALIGN=MIDDLE  ALT=\"C%5B8%5D%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > =  56 different ways to select 3 appetizers from 8 appetizers.\r\n" );
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document.write( "There are  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B9%5D%5E5 ALIGN=MIDDLE  ALT=\"C%5B9%5D%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 126 different ways to select 5 main​ courses from 9 main​ courses.\r\n" );
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document.write( "There are  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B7%5D%5E3 ALIGN=MIDDLE  ALT=\"C%5B7%5D%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > =  35 different ways to select desserts main​ courses from 7 desserts.\r\n" );
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document.write( "In all, there are 56*126*35 = 246960 different ways to select the entire meal of 3 components.   <U>ANSWER</U>\r\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "This problem uses &nbsp;COMBINATIONS &nbsp;and &nbsp;Fundamental counting principle.\r<BR>\n" );
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document.write( "On these conceptions and technique, &nbsp;see the 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/Fundamental-counting-principle-problems.lesson>Fundamental counting principle problems</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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document.write( " </SPAN>\n" );
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