document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1195868>Question 1195868</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1: A figure skating coach has 20 athletes and wishes to select 8 to take to a training trip. How many different ways could he select these 8 athletes?\r<BR>\n" );
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document.write( "2: The figure skating coach decides to enter 6 athletes into a competition. If no ties are allowed, how many different top-two orders are possible for these 6 athletes? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #828457 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=828457\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
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document.write( "(1)  There are  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B20%5D%5E8 ALIGN=MIDDLE  ALT=\"C%5B20%5D%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820%2A19%2A18%2A17%2A16%2A15%2A14%2A13%29%2F%281%2A2%2A3%2A4%2A5%2A6%2A7%2A8%29 ALIGN=MIDDLE  ALT=\"%2820%2A19%2A18%2A17%2A16%2A15%2A14%2A13%29%2F%281%2A2%2A3%2A4%2A5%2A6%2A7%2A8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 125970 different ways to select 8 athletes from 20 athletes.    <U>ANSWER</U>\r\n" );
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document.write( "It is the number of combinations of 20 persons taken 8 at a time.\r\n" );
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document.write( "Notice that the order of selection does not matter in this problem - therefore, we use COMBINATIONS.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved, answered and explained.\r<BR>\n" );
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document.write( "On &nbsp;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( "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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