document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170072>Question 1170072</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Steve wants to download a selection of new music. How many ways can Steve select four rock songs, three alternative songs, and eleven rap songs from a list of five rock songs, eight alternative songs, and twelve rap songs? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851263 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=851263\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's break down this problem using combinations.\r<BR>\n" );
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document.write( "**1. Selecting Rock Songs:**\r<BR>\n" );
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document.write( "* Steve needs to select 4 rock songs from a list of 5 rock songs.<BR>\n" );
document.write( "* This is a combination problem, as the order in which he selects the songs doesn't matter.<BR>\n" );
document.write( "* The number of ways to choose 4 rock songs from 5 is given by the combination formula:<BR>\n" );
document.write( "    * ⁵C₄ = 5! / (4! * (5-4)!) = 5! / (4! * 1!) = (5 * 4 * 3 * 2 * 1) / ((4 * 3 * 2 * 1) * 1) = 5\r<BR>\n" );
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document.write( "**2. Selecting Alternative Songs:**\r<BR>\n" );
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document.write( "* Steve needs to select 3 alternative songs from a list of 8 alternative songs.<BR>\n" );
document.write( "* The number of ways to choose 3 alternative songs from 8 is:<BR>\n" );
document.write( "    * ⁸C₃ = 8! / (3! * (8-3)!) = 8! / (3! * 5!) = (8 * 7 * 6) / (3 * 2 * 1) = 56\r<BR>\n" );
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document.write( "**3. Selecting Rap Songs:**\r<BR>\n" );
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document.write( "* Steve needs to select 11 rap songs from a list of 12 rap songs.<BR>\n" );
document.write( "* The number of ways to choose 11 rap songs from 12 is:<BR>\n" );
document.write( "    * ¹²C₁₁ = 12! / (11! * (12-11)!) = 12! / (11! * 1!) = 12\r<BR>\n" );
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document.write( "**4. Total Number of Ways:**\r<BR>\n" );
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document.write( "* To find the total number of ways Steve can select the songs, we multiply the number of ways for each genre:<BR>\n" );
document.write( "    * Total ways = ⁵C₄ * ⁸C₃ * ¹²C₁₁<BR>\n" );
document.write( "    * Total ways = 5 * 56 * 12<BR>\n" );
document.write( "    * Total ways = 3360\r<BR>\n" );
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document.write( "**Therefore, there are 3360 ways Steve can select the songs.**<BR>\n" );
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