document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=924409>Question 924409</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A group of 12 people need to form a line. The line will consist of exactly 9 of the people. Person X and Person Y have to be either third or fourth in line. How many different orders are possible? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #560806 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=560806\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> what i think is:\r<BR>\n" );
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document.write( "if x and y have to occupy the third and fourth slot, that leaves 7 slots for the other 10 people.\r<BR>\n" );
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document.write( "instead of 12P9, you get 10P7 * 2P2\r<BR>\n" );
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document.write( "10P7 = 10*9*8*7*6*5*4 = 603800\r<BR>\n" );
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document.write( "2P2 = 2*1 = 2\r<BR>\n" );
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document.write( "10P7 * 2P2 = 603800 * 2 = 1209600\r<BR>\n" );
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document.write( "the 10P7 takes care of the number of arrangements for the 10 remaining people in 7 remaining slots.\r<BR>\n" );
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document.write( "the 2P1 takes care of the number of arrangements for the 2 people in 2 slots.\r<BR>\n" );
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document.write( "to see this with smaller numbers, consider 6 people for 4 slots where x and y have to be in position 1 and 2.\r<BR>\n" );
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document.write( "instead of 6P4 = 360 possible arrangements, you have 2P2 * 4P2 = 24 possible arrangements.\r<BR>\n" );
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document.write( "let the people be xy1234\r<BR>\n" );
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document.write( "x is a person, y is a person, 1 is a person, 2 is a person, etc.\r<BR>\n" );
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document.write( "x and y have to be in positions 1 and 2, so those positions are filled.\r<BR>\n" );
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document.write( "the possible positions are:\r<BR>\n" );
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document.write( "xy12<BR>\n" );
document.write( "xy13<BR>\n" );
document.write( "xy14<BR>\n" );
document.write( "xy23<BR>\n" );
document.write( "xy24<BR>\n" );
document.write( "xy34\r<BR>\n" );
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document.write( "yx12<BR>\n" );
document.write( "yx13<BR>\n" );
document.write( "yx14<BR>\n" );
document.write( "yx23<BR>\n" );
document.write( "yx24<BR>\n" );
document.write( "yx34\r<BR>\n" );
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document.write( "xy21<BR>\n" );
document.write( "xy31<BR>\n" );
document.write( "xy41<BR>\n" );
document.write( "xy32<BR>\n" );
document.write( "xy42<BR>\n" );
document.write( "xy43\r<BR>\n" );
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document.write( "yx21<BR>\n" );
document.write( "yx31<BR>\n" );
document.write( "yx41<BR>\n" );
document.write( "yx32<BR>\n" );
document.write( "yx42<BR>\n" );
document.write( "yx43\r<BR>\n" );
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document.write( "that's a total of 24.\r<BR>\n" );
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document.write( "the formula appears to work so it can be applied to the larger problem.\r<BR>\n" );
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document.write( "the solution appears to be:\r<BR>\n" );
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document.write( "10P7 * 2P2 = 1209600\r<BR>\n" );
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document.write( "x and y have to be in positions 2 and 3<BR>\n" );
document.write( "that leaves only 1 position for a and b and c\r<BR>\n" );
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document.write( "the possible arrangements are:\r<BR>\n" );
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document.write( "axy<BR>\n" );
document.write( "bxy<BR>\n" );
document.write( "cxy<BR>\n" );
document.write( "ayx<BR>\n" );
document.write( "byx<BR>\n" );
document.write( "cyx\r<BR>\n" );
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document.write( "there are no other possible arrangements.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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