document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=927995>Question 927995</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are ten questions on a test. The instruction say that only seven of the questions are to be answered. How many ways can the seven to be answered be selected? Hint: The order in which the seven questions are answered is not important. All that matters is which seven are eventually answered. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #563381 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=563381\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is the same as asking \"How many ways are there to pick 3 questions to NOT answer\". This is easier because 3 is less than 7. Let's say we have 3 slots for the 3 questions we don't answer.\r<BR>\n" );
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document.write( "10 problems to choose from for slot 1<BR>\n" );
document.write( "9 problems to choose from for slot 2<BR>\n" );
document.write( "8 problems to choose from for slot 3\r<BR>\n" );
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document.write( "10*9*8 = 720 ways to pick 3 problems where order matters\r<BR>\n" );
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document.write( "Divide by 3! = 3*2*1 = 6 to get 720/6 = 120\r<BR>\n" );
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document.write( "There are 120 ways to select 3 problems that will NOT be attempted. The other 7 will be done.\r<BR>\n" );
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document.write( "So there are 120 ways to pick 7 problems where order doesn't matter. The final answer is <font size=5 color=\"red\">120</font>\r<BR>\n" );
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document.write( "Notice how 10 C 7 = 10 C 3 = 120 and how this symmetry shows up in Pascal's Triangle.\r<BR>\n" );
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document.write( "Jim\r<BR>\n" );
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