document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1068793>Question 1068793</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You have 5 songs by Adele and 3 by Lady Gaga and wish to make a playlist. (A playlist is just an ordering of your 8 songs.\r<BR>\n" );
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document.write( "How many playlists are possible in which no two Lady Gaga songs are consecutive? (Hint:<BR>\n" );
document.write( "Consider choosing the Adele playlist first, then counting the ways Gaga songs could be inserted.)<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 #684196 by </B><A HREF=/tutors/aboutme.mpl?userid=trsomas23@gmail.com><B>trsomas23@gmail.com(17)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=trsomas23@gmail.com><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=trsomas23@gmail.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=684196\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The 5 songs of Adele can be arranged in 5! = 120 ways<BR>\n" );
document.write( "In any arrangement of the 5 songs of Adele, there are 6 slots left: 4 in between, 1 in the beginning and 1 at the end.<BR>\n" );
document.write( "If Lady Gaga's songs are inserted in these 6 spaces, then no two Lady Gaga's songs are consecutive.\r<BR>\n" );
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document.write( "3 songs of Lady Gaga can be arranged in 6 slots in <BR>\n" );
document.write( "6P3 = 6!/(6-3)! = 6!/3! = 120 ways\r<BR>\n" );
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document.write( "Total number of ways = 120 x 120 = 14400 (Answer)<BR>\n" );
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