document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=939432>Question 939432</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove that 6C2 + 6C3 = 7C3\r<BR>\n" );
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document.write( "Step 1    6! 6! <BR>\n" );
document.write( "         --- + --- <BR>\n" );
document.write( "         2!4! 3!3! \r<BR>\n" );
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document.write( "Step 2    6!   4*6!<BR>\n" );
document.write( "        ---- + ----- <BR>\n" );
document.write( "       4*3!3!  4*3!3! \r<BR>\n" );
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document.write( "Step 3    5*6!<BR>\n" );
document.write( "         ------ <BR>\n" );
document.write( "          4*3!3!<BR>\n" );
document.write( " Step 4   7!    7*6! <BR>\n" );
document.write( "        ---- = ----- <BR>\n" );
document.write( "        3!4!   4*3!3! <BR>\n" );
document.write( "Step 5   5*6!            7*6! <BR>\n" );
document.write( "        ----- not equal ----- <BR>\n" );
document.write( "        4*3!3!           4*3!3! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #573217 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20055)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=573217\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "Prove that 6C2 + 6C3 = 7C3\r\n" );
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document.write( "That is prove that\r\n" );
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document.write( "        6!         6!         7!\r\n" );
document.write( "     -------- + -------- = --------\r\n" );
document.write( "     2!(6-2)!   3!(6-3)!   3!(7-3)!         \r\n" );
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document.write( "which simplifies to:\r\n" );
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document.write( "          6!    6!     7!\r\n" );
document.write( "         --- + ---- = ----\r\n" );
document.write( "         2!4!  3!3!   3!4!\r\n" );
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document.write( "Step 1    6!    6! \r\n" );
document.write( "         --- + ---- \r\n" );
document.write( "         2!4!  3!3! \r\n" );
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document.write( "Your first fraction is wrong on step 2. You needed a\r\n" );
document.write( "3 factor to make the 2! into a 3!\r\n" );
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document.write( "Step 2    6!   4*6!               3*6!       4*6!\r\n" );
document.write( "        ---- + ----- should be --------  +  -----\r\n" );
document.write( "       4*3!3!  4*3!3!          3*2!4*3!     4*3!3! \r\n" );
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document.write( "Step 3                            3*6!       4*6!     \r\n" );
document.write( "                               --------  +  -----\r\n" );
document.write( "                                  3!4!       4!3!\r\n" );
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document.write( "Step 4                            3*6! + 4*6! \r\n" );
document.write( "                                 -------------\r\n" );
document.write( "                                     3!4!\r\n" );
document.write( "                                \r\n" );
document.write( "Step 5                               7*6!\r\n" );
document.write( "                                    ------\r\n" );
document.write( "                                     3!4!\r\n" );
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document.write( "Step 6                                7! \r\n" );
document.write( "                                    ------\r\n" );
document.write( "                                     3!4!\r\n" );
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document.write( "Edwin</PRE>\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );