document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=758671>Question 758671</A>: <I><SPAN STYLE=\"word-break: break-all;\"> there are 5 boys and 3 girls .in how many ways can they stand in a row so that no girls are together<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 #852528 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3828)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=852528\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answer: <font color=red>14400</font>\r<BR>\n" );
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document.write( "Explanation<BR>\n" );
document.write( "There are 5 boys and 5! = 5*4*3*2*1 = 120 ways to arrange the boys.\r<BR>\n" );
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document.write( "Let's give the boys names such as:<BR>\n" );
document.write( "Alex<BR>\n" );
document.write( "Bill<BR>\n" );
document.write( "Carl<BR>\n" );
document.write( "Dave<BR>\n" );
document.write( "Eddy<BR>\n" );
document.write( "Or simply A,B,C,D,E for short.\r<BR>\n" );
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document.write( "Place blank markers between each pair of adjacent letters.<BR>\n" );
document.write( "Also, place blanks at the start and end of the sequence.\r<BR>\n" );
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document.write( "We'll have this<BR>\n" );
document.write( "_, A, _, B, _, C, _, D, _, E, _\r<BR>\n" );
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document.write( "Each blank space represents a possible spot for a girl to be placed.<BR>\n" );
document.write( "This is to guarantee the girls are not together (i.e there aren't any girls paired up nor are the 3 girls in one block).\r<BR>\n" );
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document.write( "There are 5 boys and 5+1 = 6 blank slots.<BR>\n" );
document.write( "Use the nCr combination formula to determine there are 6C3 = 20 ways to select the 3 blank slots.\r<BR>\n" );
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document.write( "Once a blank slot trio is selected, there would be 3! = 3*2*1 = 6 ways to arrange the girls in those slots.\r<BR>\n" );
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document.write( "To recap quickly:<BR>\n" );
document.write( "120 ways to arrange the boys<BR>\n" );
document.write( "20 ways to pick the 3 blank slots<BR>\n" );
document.write( "6 ways to arrange the girls for any given slot trio selection\r<BR>\n" );
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document.write( "Therefore we have 120*20*6 = <font color=red>14400</font> different arrangements where the girls are not together, i.e. no girls are next to each other.<BR>\n" );
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