document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184518>Question 1184518</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At the ice cream shop, there are 27 flavors of ice cream available. How many<BR>\n" );
document.write( "ways can you select a bowl of 5 scoops of ice cream if each scoop is a<BR>\n" );
document.write( "different flavor?<BR>\n" );
document.write( "Your answer is : <BR>\n" );
document.write( "  <BR>\n" );
document.write( "The ice cream shop has 8 types of toppings available, and you decide to add<BR>\n" );
document.write( "4 toppings to your bowl of 5 scoops of ice cream. How many combinations of 5<BR>\n" );
document.write( "scoops of ice cream and 4 toppings are possible?<BR>\n" );
document.write( "Your answer is : <BR>\n" );
document.write( "   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #815131 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20055)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=815131\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> At the ice cream shop, there are 27 flavors of ice cream available. How many<BR>\n" );
document.write( "ways can you select a bowl of 5 scoops of ice cream if each scoop is a<BR>\n" );
document.write( "different flavor?<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "We will assume that the order in which the flavors are arranged in the bowl\r\n" );
document.write( "doesn't matter, so it's COMBINATIONS, not PERMUTATIONS.\r\n" );
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document.write( "The COMBINATIONS of 27 flavors taken 5 scoops at a time is 27C5 or C(27,5)\r\n" );
document.write( "or <sub>27</sub>C<sub>5</sub> or <sup>27</sup>C<sub>5</sub> or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C1%2C27%2C5%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C1%2C27%2C5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is\r\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2827%2A26%2A25%2A24%2A23%29%2F%285%2A4%2A3%2A2%2A1%29=80730 ALIGN=MIDDLE  ALT=\"%2827%2A26%2A25%2A24%2A23%29%2F%285%2A4%2A3%2A2%2A1%29=80730\"   DISABLED_style= \"max-width:90%; height:auto;\" > ways.</PRE>  <BR>\n" );
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document.write( "The ice cream shop has 8 types of toppings available, and you decide to add<BR>\n" );
document.write( "4 toppings to your bowl of 5 scoops of ice cream. How many combinations of 5<BR>\n" );
document.write( "scoops of ice cream and 4 toppings are possible?<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "For each of those 80730 ways to have 5 flavors, there are all the\r\n" );
document.write( "COMBINATIONS of 8 toppings taken 4 at a time, which is 8C4 or C(8,4)\r\n" );
document.write( "or <sub>8</sub>C<sub>4</sub> or <sup>8</sup>C<sub>4</sub> or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C1%2C8%2C4%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C1%2C8%2C4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2A7%2A6%2A5%29%2F%284%2A3%2A2%2A1%29=70 ALIGN=MIDDLE  ALT=\"%288%2A7%2A6%2A5%29%2F%284%2A3%2A2%2A1%29=70\"   DISABLED_style= \"max-width:90%; height:auto;\" > ways for the toppings, so \r\n" );
document.write( "(80730)(70) = 5651100 ways for ice cream and toppings.\r\n" );
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document.write( "Edwin</PRE> </SPAN>\n" );
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