document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1155078>Question 1155078</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A student must answer 7 questions on a 12 question test.  How many ways can a student do this, and how many ways are there if the student must answer the first and last questions? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #777631 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52787)</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=777631\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
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document.write( "The student can select 7 questions from 12 questions by  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B12%5D%5E7 ALIGN=MIDDLE  ALT=\"C%5B12%5D%5E7\"   DISABLED_style= \"max-width:90%; height:auto;\" > ways.\r\n" );
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document.write( "It is the number of combinations of 12 items taken 7 at a time.\r\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B12%5D%5E7 ALIGN=MIDDLE  ALT=\"C%5B12%5D%5E7\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%21%2F%287%21%2A5%21%29 ALIGN=MIDDLE  ALT=\"12%21%2F%287%21%2A5%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%2A11%2A10%2A9%2A8%29%2F%281%2A2%2A3%2A4%2A5%29 ALIGN=MIDDLE  ALT=\"%2812%2A11%2A10%2A9%2A8%29%2F%281%2A2%2A3%2A4%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r\n" );
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document.write( "Calculate it using your calculator.\r\n" );
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document.write( "Answered, and you are instructed and directed.\r<BR>\n" );
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document.write( "On Combinations, &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/Math-circle-level-problem-on-Combinations.lesson>Math circle level problem 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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document.write( " </SPAN>\n" );
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