document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=673995>Question 673995</A>: <I><SPAN STYLE=\"word-break: break-all;\">  A disc jockey has 9 songs to play. Five are slow songs, and 4 are fast songs.  Each song is to be played only once.  In how many ways can the disc jockey play the 9 songs if<BR>\n" );
document.write( "The songs can be played in any order. <BR>\n" );
document.write( "The first song must be a slow song and the last song must be a slow song. <BR>\n" );
document.write( "The first two songs must be fast songs.\r<BR>\n" );
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document.write( "Can you please explain this as you go. I not just out for an easy answer, I need insturction.PLEASE </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #418977 by </B><A HREF=/tutors/aboutme.mpl?userid=chandrumail><B>chandrumail(4)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=chandrumail><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=418977\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) The songs can be played in any order:\r<BR>\n" );
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document.write( "    No of ways the 9 songs can be played = 9! = 362880\r<BR>\n" );
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document.write( "Explanation: the 1st song can be chosen from any of the 9 songs, the 2nd played song can be chosen from the remanining 8 songs, the 3rd played song can be chosen from the remaining 6 songs, the 5th played song can be chosen from the remaining 5 songs, the 6th played song can be chosen from the remaining 4 songs, the 7th played song can be chosen from the remaining 3 songs, the 8th played song can be chosen from the remaining 2 songs and the 9th played song can be chosen from the remaining 1 song. Hence the no of ways = 9*8*7*....2*1 =9!\r<BR>\n" );
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document.write( "2) The first song must be a slow song and the last song must be a slow song.\r<BR>\n" );
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document.write( "No of ways the 1st song can be chosen = 5 (as there are 5 slow songs)<BR>\n" );
document.write( "No of ways the 9th song can be chosen = 4 (as there are 4 remaining slow songs left) \r<BR>\n" );
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document.write( "Having chosen the 1st and 9th, the songs 2 thru 8 can be chosen in 7! ways\r<BR>\n" );
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document.write( "Total no of ways = 7!*5*4 = 100800 ways\r<BR>\n" );
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document.write( "3) The first two songs must be fast songs.\r<BR>\n" );
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document.write( "No of ways to select 1st song = 4 (as there are 4 fast songs)<BR>\n" );
document.write( "No of ways to select 2nd song = 3 (as there are remaining 3 fast songs)\r<BR>\n" );
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document.write( "Having chosen 1st and 2nd song, the songs 3 thru 9 can be chosen in 7! ways\r<BR>\n" );
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document.write( "Total no of ways = 7!*4*3 = 60480\r<BR>\n" );
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