document.write( "Question 85850: Please help me find a solution to this problem\r
\n" ); document.write( "\n" ); document.write( "Blue-Bunny Ice Cream, sells 31 flavors.
\n" ); document.write( "A.) How many 2-dip cones are possible if order of flavors is to be considered and no flavor is repeated?
\n" ); document.write( "B.) How many 2-dip cones are possible if order of flavors is to be considered and flavors CAN be repeated.
\n" ); document.write( "C.) How many 2-dip cones are possible if order is NOT considered and NO flavor is repeated?\r
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Algebra.Com's Answer #62046 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
Please help me find a solution to this problem \r\n" );
document.write( "Blue-Bunny Ice Cream, sells 31 flavors.\r\n" );
document.write( "A.) How many 2-dip cones are possible if order of flavors is to be considered\r\n" );
document.write( "and no flavor is repeated?\r\n" );
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document.write( "Choose the bottom dip 31 ways. For every one of these you may choose\r\n" );
document.write( "the top dip 30 ways.  That's 31·30 or 930 ways.  That counts, for instance,\r\n" );
document.write( "vanilla on the bottom and chocolate on top as a separate cone from\r\n" );
document.write( "chocolate on the bottom and vanilla on top. \r\n" );
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document.write( "B.) How many 2-dip cones are possible if order of flavors is to be considered\r\n" );
document.write( "and flavors CAN be repeated.\r\n" );
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document.write( "This is a difficult problem.  This involves advanced combinatorics.\r\n" );
document.write( "I don't think your teacher or textbook author should expect you to be able to\r\n" );
document.write( "do this one because it involves a summation over all the ways you can have\r\n" );
document.write( "k repeated flavors and 31-k non-repeated flavors for 0 < k < 31.  I think \r\n" );
document.write( "your teacher and/or the textbook author may have thought this to be an easier\r\n" );
document.write( "problem than it really is. \r\n" );
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document.write( "C.) How many 2-dip cones are possible if order is NOT considered \r\n" );
document.write( "and NO flavor is repeated?\r\n" );
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document.write( "This is the combinations of 31 things taken 2 at a time:\r\n" );
document.write( "                        15\r\n" );
document.write( "           31·30     31·30\r\n" );
document.write( "C(31,2) = ------- = ------- = 31·15 = 465\r\n" );
document.write( "            1·2       1·2\r\n" );
document.write( "                        1  \r\n" );
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document.write( "Edwin
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