document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=109952>Question 109952</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The ice cream parlor can make a sundae using any combination of 6 toppings and 4 different types of ice cream, as shown on the menu below. <BR>\n" );
document.write( "Types of Ice Cream  Sundae Toppings  <BR>\n" );
document.write( "vanilla  hot fudge  <BR>\n" );
document.write( "chocolate  hot caramel  <BR>\n" );
document.write( "strawberry  cookie crumbs  <BR>\n" );
document.write( "coffee  nuts  <BR>\n" );
document.write( "candy pieces  <BR>\n" );
document.write( "chocolate sprinkles  \r<BR>\n" );
document.write( "\n" );
document.write( "A. Anne wants a sundae with 2 different toppings on chocolate ice cream. How many different combinations of toppings for Anne’s sundae are possible? Show your work and explain why you did each step. <BR>\n" );
document.write( "B. Will wants a sundae with 3 different toppings on any type of ice cream. How many different sundae combinations are possible? Show your work and explain why you did each step </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #80184 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=80184\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The ice cream parlor can make a sundae using any combination of 6 toppings and 4 different types of ice cream, as shown on the menu below. <BR>\n" );
document.write( "Types of Ice Cream  Sundae Toppings  <BR>\n" );
document.write( "vanilla  hot fudge  <BR>\n" );
document.write( "chocolate  hot caramel  <BR>\n" );
document.write( "strawberry  cookie crumbs  <BR>\n" );
document.write( "coffee  nuts  <BR>\n" );
document.write( "candy pieces  <BR>\n" );
document.write( "chocolate sprinkles  \r<BR>\n" );
document.write( "\n" );
document.write( "A. Anne wants a sundae with 2 different toppings on chocolate ice cream. How many different combinations of toppings for Anne’s sundae are possible? Show your work and explain why you did each step. <BR>\n" );
document.write( "----------<BR>\n" );
document.write( "6C2 = 6*5/1*2 = 15<BR>\n" );
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document.write( "There are 6 ways to choose the 1st topping and 5 ways to choose the 2nd<BR>\n" );
document.write( "topping.  There there are 30 arrangements of 2 toppings. But each pair <BR>\n" );
document.write( "of toppings appears twice in the list of arrangements: for example,the<BR>\n" );
document.write( "pair coffee nots/candy pieces appears appears twice but is only one pair.<BR>\n" );
document.write( "So dividing all the arrangements by 2 gives 15 pairs (or combinations)<BR>\n" );
document.write( "of two toppings.<BR>\n" );
document.write( "----------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "B. Will wants a sundae with 3 different toppings on any type of ice cream. How many different sundae combinations are possible? Show your work and explain why you did each step<BR>\n" );
document.write( "6C3 = 6*5*4/1*2*3= 20<BR>\n" );
document.write( "Same reasoning as above: 120 arrangements but 6 ways to arrange the three<BR>\n" );
document.write( "elements of each group (combination).<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );