document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=968110>Question 968110</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how many ways there are to remove three elements from the sequence  1 4 2 5 7 3 8 9, so that the remaining from an increasing sequence\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #692244 by </B><A HREF=/tutors/aboutme.mpl?userid=quixote><B>quixote(1)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=quixote><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=692244\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Make a graph of the sequence, it will help to visualize\r<BR>\n" );
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document.write( "We need to keep 5 numbers:\r<BR>\n" );
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document.write( "Case 1: begin with 1 (<BR>\n" );
document.write( " case1A:  begin with 14 and choose 3 from (5789)----> 4 ways<BR>\n" );
document.write( " case1B1: begin with 12 and choose 3 from (5789)----> 4 ways<BR>\n" );
document.write( " case1B2: begin with 123 and then we left with (89)---> 1 way<BR>\n" );
document.write( " case1C:  begin with 15 and then we left with (789)----> 1 way\r<BR>\n" );
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document.write( "Case 2: Begin with 4 and then we left with (5789) -----> 1 way<BR>\n" );
document.write( "Case 3: Begin with 2 and then we again left with (5789)----> 1 way\r<BR>\n" );
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document.write( "Hence total #ways = 12 </SPAN>\n" );
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