document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=352388>Question 352388</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 10 people line up for a photo, including you and your friend. How many line arrangements are there if the photographer insists on keeping 3 people in between you and your friend? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #252130 by </B><A HREF=/tutors/aboutme.mpl?userid=nyc_function><B>nyc_function(2741)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nyc_function><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=nyc_function><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=252130\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are 10 people: A(you), B(your friend) and 8 others.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You and your friend are spaced like this:\r<BR>\n" );
document.write( "\n" );
document.write( "A____B or B____A = two ways\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Select 3 of the Others and arrange them in the spaces. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "There are: 8P3 = 8!/5! = 336 ways.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now we have 6 \"people\" to arrange: AxyzB and 5 others.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "There are: 6! = 720 ways.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Therefore, there are: 2 * 336 * 720 = 483,840 line arrangements.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );