document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=265745>Question 265745</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If you have 5 types of flowers (roses, lilacs, lillys, daffodils and tulips), and your business model is to sell them prepackaged in vases.  Each vase must contain 3 different types of flowers (no repeats).  How many combinations can you acheive? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #195362 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=195362\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "Presuming order doesn't matter -- that is a vase with a rose, a lilac, and a lily is only one possibility regardless of whether the rose, the lilac, or the lily went into the vase first -- then you need the number of ways to select 3 things from 5 things.\r<BR>\n" );
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document.write( "The number of ways to select <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large r\"> things from a collection of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\"> things is given by:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(n\cr r\right)\ =\ \frac{n!}{r!(n\,-\,r)!}\">\r<BR>\n" );
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document.write( "In your case:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(5\cr 3\right)\ =\ \frac{5!}{3!(5\,-\,3)!}\ =\ \frac{5!}{3!2!}\ =\ \frac{5\,\cdot\,4\,\cdot\,3\,\cdot\,2\,\cdot\,1}{(3\,\cdot\,2\,\cdot\,1)(2\,\cdot\,1)}\">\r<BR>\n" );
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document.write( "You can do your own arithmetic.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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